Scaling Laws
Mathematical relationships describing how properties change with size. Many biological and organizational properties scale predictably with organism or company size.
Used in the Books
This term appears in 5 chapters:
"... Wrong. Kleiber found that metabolic rate scales with body mass to the 3/4 power. This is now called Kleiber's Law, and it's one of the most robust scaling laws in biology. The formula is: Metabolic Rate = M^0.75 Where M is body mass. What does this mean in practice? An animal that weighs 1,000 times m..."
"M., et al. (1999). "Optimizing the success of random searches." Nature, 401(6756), 911-914. - Sims, D. W., et al. (2008). "Scaling laws of marine predator search behaviour." Nature, 451(7182), 1098-1102. - Stephens, D. W., & Krebs, J. R. (1986). Foraging Theory."
"...ered that metabolism doesn't scale with mass (M^1.0) but with mass to the 3/4 power (M^0.75). This became Kleiber's Law - one of the most fundamental scaling laws in biology. Kleiber's Law: Basal metabolic rate (BMR) scales as mass^0.75. This means: - 1 kg animal: ~10 watts - 10 kg animal (10× mass): ~56 watts..."
"Book 7, Chapter 1: Scaling Laws - The Mathematics of Size Introduction Watch a shrew for five minutes and you'll witness something like controlled panic."
"...furcates, and daughter roots explore different soil regions, maximizing exploration per unit root biomass. Empirically, plant root branching follows scaling laws similar to Murray's Law: - Root diameter decreases by ~0.7-0.8× per branching level (similar to 2^(-1/3) ≈ 0.79 in vascular systems) - Root length in..."
Biological Context
Metabolic rate scales with body mass^0.75. Lifespan scales with mass^0.25. Heart rate scales with mass^-0.25. These relationships hold across enormous size ranges, suggesting fundamental constraints on biological organization.
Business Application
Business scaling laws describe how costs, revenue, and efficiency change with company size. Understanding these relationships helps set realistic growth expectations.