Square-Cube Law
Organizations face equivalent structural limits.
You can't just scale a successful small structure linearly. At each size increase, fundamental redesigns become necessary. Physics doesn't care about your growth plans.
Volume (and mass) increase as the cube of linear dimensions, but surface area (and structural support) increase only as the square. Scale an ant to elephant size (10,000× linear dimensions), and it collapses under its own weight. The ant's legs, which easily support its tiny mass, would need to be 100× thicker (relative to body size) to support the scaled-up mass.
Support capacity = strength / mass = length² / length³ = 1/length. Double an animal's size, and each leg can support only half as much weight per unit mass. This is why elephants (6 tons) have legs like tree trunks - thick, columnar, with minimal bending. Elephants can't jump. The largest land animal ever was Patagotitan mayorum at 77 tons with pneumatic (air-filled) bones. Blue whales reach 150-180 tons only because water supports their weight via buoyancy.
Business Application of Square-Cube Law
Organizations face equivalent structural limits. As companies grow, coordination costs increase faster than productive capacity. The 'organizational weight' of decision-making layers, communication overhead, and complexity eventually exceeds the 'structural support' of management systems.
Discovery
Galileo Galilei (1638)
First articulation that giant animals couldn't simply be scaled-up versions of small animals - their bones would shatter under their own weight
Square-Cube Law Appears in 3 Chapters
The square-cube law explains why elephants have tree-trunk legs and can't jump - structural support capacity decreases relative to mass as size increases.
Square-cube law in biology →Surface area grows as the square while volume grows as the cube, creating cascading problems for heat dissipation, structural support, and resource delivery.
Geometric constraints on growth →Galileo's 1638 insight - giant animals can't be scaled-up small animals - explains why large organizations need disproportionate coordination infrastructure.
Galileo's scaling insight →