The Asymmetry of Totalizing Ideals: A Structural Law of Complex Adaptive Systems

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1. Verfasser: Kriger, Boris
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author Kriger, Boris
author_facet Kriger, Boris
contents <p>This paper proves a structural impossibility theorem for complex adaptive systems: under irreducible uncertainty, the pursuit of a terminal, globally optimal, and fully coherent target state produces unbounded expected long-term damage, while maintenance of a boundedly suboptimal variance-preserving state yields finite damage.</p> <p>The proof employs a rigorous information-theoretic framework:</p> <ul> <li>Adaptive variance is defined as mutual information between state distribution and unknown environmental parameters: V_t := I(π_t; θ*)</li> <li>An explicit loss functional connects variance, accumulated model error, and systemic damage</li> <li>The main theorem is proved by showing that totalizing optimization drives variance to zero, exhausting the system's learning capacity before model errors can be corrected, leading to divergent damage</li> </ul> <p>Key contributions:</p> <ol> <li>Rigorous definitions grounded in Shannon information theory</li> <li>Explicit "insufficient learning capacity" condition: ‖θ̂₀ − θ*‖² > κV₀/α</li> <li>Complete proof with explicit functional forms</li> <li>Clear necessary and boundary conditions ensuring falsifiability</li> <li>Two corollaries: the Optimization Dominance Law ("best is enemy of good") and mechanistic foundation for the Law of Imperative Uncertainty</li> </ol> <p>The theorem unifies insights from complexity science (Kauffman, Ashby), information theory (Cover & Thomas), political philosophy (Hayek, Scott), and evolutionary biology (Fisher) under a single mechanistic framework. An epilogue demonstrates that biological evolution's persistent maintenance of suboptimality is a direct consequence of the theorem—explaining why nature does not strive for perfection.</p> <p><strong>Keywords:</strong> complex adaptive systems, information theory, mutual information, Shannon entropy, optimization theory, adaptive variance, totalizing ideals, systemic resilience, irreducible uncertainty, Ashby's law of requisite variety</p> <p> </p>
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spellingShingle The Asymmetry of Totalizing Ideals: A Structural Law of Complex Adaptive Systems
Kriger, Boris
complex adaptive systems
information theory
mutual information
Shannon entropy
optimization theory
adaptive variance
totalizing ideals
systemic resilience
irreducible uncertainty
Ashby's law of requisite variety
<p>This paper proves a structural impossibility theorem for complex adaptive systems: under irreducible uncertainty, the pursuit of a terminal, globally optimal, and fully coherent target state produces unbounded expected long-term damage, while maintenance of a boundedly suboptimal variance-preserving state yields finite damage.</p> <p>The proof employs a rigorous information-theoretic framework:</p> <ul> <li>Adaptive variance is defined as mutual information between state distribution and unknown environmental parameters: V_t := I(π_t; θ*)</li> <li>An explicit loss functional connects variance, accumulated model error, and systemic damage</li> <li>The main theorem is proved by showing that totalizing optimization drives variance to zero, exhausting the system's learning capacity before model errors can be corrected, leading to divergent damage</li> </ul> <p>Key contributions:</p> <ol> <li>Rigorous definitions grounded in Shannon information theory</li> <li>Explicit "insufficient learning capacity" condition: ‖θ̂₀ − θ*‖² > κV₀/α</li> <li>Complete proof with explicit functional forms</li> <li>Clear necessary and boundary conditions ensuring falsifiability</li> <li>Two corollaries: the Optimization Dominance Law ("best is enemy of good") and mechanistic foundation for the Law of Imperative Uncertainty</li> </ol> <p>The theorem unifies insights from complexity science (Kauffman, Ashby), information theory (Cover & Thomas), political philosophy (Hayek, Scott), and evolutionary biology (Fisher) under a single mechanistic framework. An epilogue demonstrates that biological evolution's persistent maintenance of suboptimality is a direct consequence of the theorem—explaining why nature does not strive for perfection.</p> <p><strong>Keywords:</strong> complex adaptive systems, information theory, mutual information, Shannon entropy, optimization theory, adaptive variance, totalizing ideals, systemic resilience, irreducible uncertainty, Ashby's law of requisite variety</p> <p> </p>
title The Asymmetry of Totalizing Ideals: A Structural Law of Complex Adaptive Systems
topic complex adaptive systems
information theory
mutual information
Shannon entropy
optimization theory
adaptive variance
totalizing ideals
systemic resilience
irreducible uncertainty
Ashby's law of requisite variety
url https://doi.org/10.5281/zenodo.18361828