Technical
Formula derivation, version history, and implementation details.
Formula Derivation
v9.3.2 (Current)
Structural base: φ × τ × ρ
Multiplicative relationship. Zero in any dimension produces zero density.
Entropy penalty: (1 - √H)
Square root provides nonlinear sensitivity. Low entropy (H=0.1) yields 0.68. High entropy (H=0.9) yields 0.05.
Coherence recovery: (H × κ)
High entropy with high coherence recovers density. This resolves the DMT paradox.
Entropy modulator: [(1 - √H) + (H × κ)]
Combines penalty and recovery. Range: 0 to ~1.5 depending on H and κ values.
Why multiplicative, not additive?
Additive models (D = φ + τ + ρ) allow compensation. A system with φ=0, τ=1, ρ=1 would have D=2/3. This predicts that a system with zero integration can still have substantial perspective.
Multiplicative models enforce necessity. If integration is zero, there is no unified perspective, regardless of other dimensions. This matches intuition: you cannot have perspective without something to have perspective of.
The dimensional collapse test (experiments/260114_Break_Tests) confirms this: all 2D configurations produce zero density.
Why square root for entropy?
Tested models: linear (1-H), quadratic (1-H²), square root (1-√H), exponential (e^-H).
Square root provides optimal differentiation between states. Flow state (H=0.2) vs Panic state (H=0.8) differentiation is 1566x better than v7.0 (no entropy term).
Source: experiments/260114_Entropy_Integration_Models.md
Why add coherence?
v8.0 predicted DMT breakthrough (H=0.95) would have density near zero. Phenomenological reports describe "hyper-consciousness," not dissolution.
The problem: entropy alone cannot distinguish structured chaos (DMT, high κ) from destructive noise (seizure, low κ).
Solution: coherence gate. H × κ recovers density when entropy is high but structured.
Seizure: H=0.95, κ=0.10 → D=0.01
Source: experiments/260114_DMT_Paradox_Resolution_Synthesis.md
Version History
Current version. Isocline degeneracy analysis, error propagation framework, confidence badges. Corrected all CANON D-values to match formula output.
κ validated via Multi-Scale Entropy (r=0.987). AT08-AT11 extended validation. φ upgraded to MODERATE-HIGH confidence via multi-metric anchoring.
Calibrated parameter values from neuroscience literature. Empirical anchors established for all five invariants.
Integrates all experimental findings. Includes RWKV validation, Transformer falsification, and coherence gate. Rewritten for clarity.
Added coherence dimension (κ) to resolve DMT paradox. Formula: D = φ × τ × ρ × [(1 - √H) + (H × κ)].
Added entropy dimension (H). Formula: D = φ × τ × ρ × (1 - √H). Fixed corporate consciousness bug. Identified DMT paradox.
Three-dimensional formula: D = φ × τ × ρ. Introduced multiplicative relationship. Had panpsychism problem (Walmart = 0.504).
Philosophical development. Established core concepts: The Source (raw experiential capacity), The Conduit (structure that shapes perspective), gradient of consciousness.
Implementation
TypeScript Engine
export interface Invariants {
phi: number; // Integration (0-1)
tau: number; // Temporal Depth (0-1)
rho: number; // Binding (0-1)
H: number; // Entropy (0-1)
kappa: number; // Coherence (0-1)
}
export function calculateDensity(invariants: Invariants): DensityResult {
const { phi, tau, rho, H, kappa } = invariants;
// Structural base (multiplicative)
const structuralBase = phi * tau * rho;
// Entropy modulation
const entropyPenalty = 1 - Math.sqrt(H);
const coherenceRecovery = H * kappa;
const entropyModulator = entropyPenalty + coherenceRecovery;
// Final density
const D = structuralBase * entropyModulator;
return {
D: Math.max(0, Math.min(1, D)),
structuralBase,
entropyPenalty,
coherenceRecovery,
entropyModulator,
interpretation: getInterpretation(D)
};
}Python Engine
def calculate_density(phi, tau, rho, H, kappa):
"""
Calculate perspectival density from five invariants.
Args:
phi: Integration (0-1)
tau: Temporal depth (0-1)
rho: Binding (0-1)
H: Entropy (0-1)
kappa: Coherence (0-1)
Returns:
float: Perspectival density D
"""
structural_base = phi * tau * rho
entropy_penalty = 1 - math.sqrt(H)
coherence_recovery = H * kappa
entropy_modulator = entropy_penalty + coherence_recovery
D = structural_base * entropy_modulator
return max(0, min(1, D))Constraints
- • All parameters normalized to [0, 1]
- • Output D clamped to [0, 1]
- • Zero in φ, τ, or ρ produces zero D (multiplicative necessity)
- • H=0 produces maximum entropy modulator (1.0)
- • H=1, κ=0 produces minimum entropy modulator (0.0)
- • H=1, κ=1 produces entropy modulator of 1.0 (full recovery)