Murray's Law
Organizations face analogous trade-offs when designing hierarchies.
Evolution optimized transport networks independently in unrelated systems - plants, animals, geology. All converged on the identical solution because physics is universal.
Murray's Law (or cube law) predicts optimal branching in vascular networks. At each bifurcation where one vessel splits into two, the relationship between parent vessel radius r₀ and daughter vessel radii r₁, r₂ follows: r₀³ = r₁³ + r₂³. This emerges from minimizing total energy cost (metabolic cost of blood volume plus pumping cost of overcoming viscous drag). Mammalian vasculature closely follows this law across species from mice to elephants. Evolution discovered this ratio over hundreds of millions of years.
Business Application of Murray's Law
Organizations face analogous trade-offs when designing hierarchies. Wide spans of control save on hierarchy depth but create oversight challenges. Narrow spans provide better oversight but multiply layers. Murray's Law suggests there's an optimal branching ratio that minimizes total organizational 'energy costs' - the sum of oversight costs plus hierarchy costs.
Discovery
Cecil Murray (1926)
Derived mathematical principle showing that optimal branching networks minimize total cost (material + operating) through cubic scaling of vessel radii
Murray's Law Appears in 2 Chapters
Murray's Law predicts optimal branching in vascular networks - the cube relationship emerges from minimizing total energy cost of material plus pumping.
Murray's Law in fractal networks →Biological systems from blood vessels to tree xylem to river networks all converge on Murray's Law - physics is universal across scales.
Universal optimal branching →