Scaling Laws
When coordination costs grow faster than value creation, organizational failure becomes mathematically inevitable.
When coordination costs scale as N^1.8 and value scales as N^0.9, failure isn't a possibility - it's a certainty.
Scaling laws describe how properties change with size through power-law relationships: Y = aX^b, where b is the scaling exponent. When b equals one, the relationship is isometric - double the size, double the property. When b differs from one, it's allometric - double the size, and the property changes by 2^b. Most biological and organizational properties scale allometrically. Metabolic rate scales as mass^0.75. Heart rate scales as mass^-0.25. These aren't arbitrary numbers - they emerge from fundamental physical and geometric constraints including fractal-like branching networks and the square-cube law.
Business Application of Scaling Laws
Organizations exhibit scaling laws analogous to biological systems: coordination costs often scale as headcount^1.5 or worse, while revenue per employee typically scales as headcount^0.9. When coordination costs grow faster than value creation, organizational failure becomes mathematically inevitable.