Pulse Core Lexicon
Information Threshold
Definition
The Information Threshold is the reference local information density, approximately 10 bits/m³, at which the information factor of the Combined Threshold Function reaches 1.
It is the value the Information Density Criterion tests against: the local information density, measured as a Shannon entropy, must be at least I⨶. The threshold also enters the Combined Threshold Function as the denominator of the information ratio, raised to the exponent γ = 1/2, so that stable form requires Θ ≥ 1 across density, coherence and information together.
In the book's criterion I⌂ = −sum_i p_i log_2(p_i) ≥ I⨶, I⨶ is the Information Threshold, I⌂ the local information density and p_i the probability of state i. Dimensions from the book's Where-list: I⨶ and I⌂ [𝕃⁻³·1ᵇ]; the numerical value 10 [∅].
It connects to the Information Density Criterion, Combined Threshold Function, Form Emergence Condition and Critical Density Threshold.
Mathematical Expression
From the book · Chapter 7 · Thresholds of Recursion — When the Field Becomes Form
I⌂ = -sum_i p_i log_2(p_i) ≥ I⨶ [𝕃⁻³·1ᵇ]
Where:
- I⌂ [𝕃⁻³·1ᵇ] - local information density
- sum_i - summation operator over all probability states i
- p_i [∅] - probability distributions for state i
- log_2 - logarithm base 2 function
- ≥ - inequality operator, greater than or equal to
- I⨶ [𝕃⁻³·1ᵇ] - Information Threshold (G), approximately 10 bits/m³
- i [∅] - probability state index
- 10 [∅] - numerical threshold value
- [∅] - quantities without physical units, pure numerical ratios or mathematical constants
Technical Details
Category Concept
Chapter Chapter 7
Importance