The Inverse Scaling Law (ISL): In all physically realizable systems, existential cost (
) decreases monotonically as modular capability (
) increases, subject to fundamental physical constraints.
Formal Statement
Nature favors efficiency. The ISL is the mathematical formalization of this universal bias. Systems—whether biological, computational, or physical—evolve toward configurations that minimize existential cost per unit of structural capability.
Why ISL is Universal
1. Domain Independence: Operates across computation, physics, biology, mathematics, and economics.
2. Fundamental Constraint: It describes efficiency gradients within conservation laws.
3. Predictive Power: Generates testable thresholds for scaling failure.
4. Falsifiability: If a system is found where increasing structural complexity (without redundancy) reduces efficiency/capability, the law is falsified.
Intellectual Lineage
The ISL sits at the intersection of:
- Prigogine’s Non-Equilibrium Thermodynamics
- Shannon’s Information Theory
- The Bekenstein-Hawking Entropy Bounds
- Landauer’s Principle
This declaration marks the formal entry of the Inverse Scaling Law into the corpus of universal constraints.