The τ Threshold: Foundations, and Reasoning. - MUESdummy/Emergent-Necessity-Theory-ENT- GitHub Wiki

Foundations, Axioms, and Clarifications

📘 Overview

The τ threshold in ENT (Emergent Necessity Theory) marks the point at which a system’s informational coherence becomes structurally necessary for sustained order or emergence.

This page outlines:

The foundational motivation behind introducing τ
Core assumptions (axioms) ENT rests on
Mathematical rationale for choosing a threshold model
Where uncertainty or testing is still needed

1. 🔧 Why Threshold? Why Not Continuity?

Most existing models (e.g., entropy minimization in Friston’s Free Energy Principle, or integration scores in IIT) treat emergence as a continuous phenomenon.

ENT challenges this by proposing that some structural events are discontinuous, not because reality is binary—but because certain conditions, when met, require emergence to occur.

This is not a metaphysical claim. It's structural.

Example: Water doesn't boil gradually. Once thermal coherence (heat) reaches a critical threshold (100°C at 1 atm), phase transition must happen.

Likewise, ENT argues that when symbolic/structural information becomes coherent enough (via recursion, persistence, and stability), new behavior emerges not just as a likelihood—but as a necessity.

2. ⚖️ Core Axioms Underpinning ENT

These are not assumed to be absolute truths—just a minimal viable set that makes ENT function as a model:

Coherence matters more than complexity.
Systems can be complex but incoherent. ENT tracks structured recurrence, not entropy reduction.
Information has energy cost.
Especially symbolic information. Its persistence requires effort (neural, computational, societal).
Emergence occurs only when structure stabilizes. Random fluctuations ≠ emergence. Coherence sustained across layers leads to true emergence.
There exists a minimum viable coherence.
This is denoted by τ_c, the threshold point. Below it, systems decay. Above it, structure locks in.

3. 📏 What is τ (tau)?

τ (informational coherence) is a normalized, dimensionless measure:

τ = (I - H) / S

Where:

I = Mutual Information
H = Local Entropy
S = System Complexity Scaling Factor

When τ reaches or exceeds a critical threshold (denoted τ_c), new structure must emerge or existing structure must stabilize.

4. 🔬 Why a Threshold, Mathematically?

Threshold behavior arises naturally in systems governed by:

Nonlinear feedback
Phase transitions
Recursive stability
Hysteresis loops

The model maps loosely onto bifurcation theory:
Below a critical point, the system exhibits one behavior (chaos, decay); beyond it, it snaps into a new state (order, persistence).

This is mathematically supported by bifurcation diagrams, sigmoid activation curves, and thermodynamic inflection zones.

ENT applies this not to particles or chemicals—but to symbolic, neural, or social systems.

5. 🔃 Real-World Analogy: Identity Collapse

A person under stress may seem "fine" up to a point—until coherence collapses (e.g., breakdown, dissociation).
ENT would model this not as a smooth line but a threshold crossing:

Below τ_c: thoughts disintegrate, feedback loops lose stability.
Above τ_c: thoughts stabilize, self-awareness recurses.

6. 📉 What Is τ_c? Where Is It?

ENT simulations suggest different τ_c values depending on domain:

Neural systems: ~1.46 (EEG-based simulation)
Symbolic models (LLMs): ~1.8
Quantum coherence models: ~1.5
Social coherence models: ~2.1 (simulated only)

These are provisional. They reflect simulation outputs, not metaphysical constants.

ENT is built to evolve. Every τ_c is testable, revisable, and tied to structural behaviors—not ideology.

7. 🏳️ Transparency & Cautions

ENT does not claim τ is the only metric.
It is a tool for observing when order becomes necessary—not sufficient.
τ_c is not moral, not metaphysical.
It is structural. Collapse ≠ failure. Emergence ≠ superiority.
Some systems may not follow threshold behavior at all.
ENT is not universal—it’s applicable only to recursive symbolic systems.