Probability is Lack of Information: Part III - The Derivative of Binary Entropy as the Gradient of Determinism
Diğer, ss.1-8, 2026
- Yayın Türü: Diğer Yayınlar / Diğer
- Basım Tarihi: 2026
- Sayfa Sayıları: ss.1-8
- Ankara Üniversitesi Adresli: Evet
Özet
Access the Official Full Text via Elsevier-SSRN:
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=6962403
Abstract: Following the axiomatic foundation established in Part I and the formal proof via the Binary Entropy Function in Part II, this third installment introduces the derivative of the binary entropy function, H'(p) = −log₂((1−p)/p), as the Gradient of Determinism. We demonstrate that this gradient serves as a quantitative measure of the rate at which informational deficit vanishes, thereby revealing the underlying deterministic structure of reality.
The derivative reaches its maximum steepness as p → 0⁺ or p → 1⁻, where H'(p) → ±∞, indicating a near-instantaneous transition to certainty. At p = 0.5, the gradient vanishes (H'(p) = 0), corresponding to the point of maximum ignorance. We propose practical determinism thresholds (e.g., |H'(p)| ≥ 5, 10, and 20 bits) to quantify the transition from epistemic uncertainty to effective determinism.
Within the Hendeca-Tier Cosmic Signal Architecture (HCSA), this gradient provides a rigorous mathematical bridge between observer-limited probability and the absolute 121-unit mizanic determinism. By reinterpreting quantum measurement and Born’s rule through the lens of this gradient, we advance the central motto of the series: Probability is lack of information.