Amara's Law

Biological Parallel

S-curves dominate biological change because growth happens in three phases that distort perception. Bacterial cultures demonstrate this with mathematical precision: E. coli inoculated into fresh media enters lag phase for 1 hour to several days—no visible growth, but cells are synthesizing enzymes, repairing damage, and preparing metabolic machinery. Then exponential phase: populations doubling every 20 minutes for Salmonella under ideal conditions. Growth feels unlimited. Then stationary phase when nutrients deplete or waste accumulates—growth stops as births equal deaths. Each phase misleads observers who extrapolate current rates. Invasive species reveal the same pattern at ecosystem scale. The emerald ash borer demonstrated this in the U.S. with four distinct spread periods alternating between rapid and slow expansion as it encountered varying resistance. Spongy moth invasion of North America follows the misjudgment pattern precisely: rapid spread 1900-1915, slow phase 1916-1965, rapid again 1966-1990. Observers in each phase extrapolated current rates and were systematically wrong. During lag phases, threats seem overblown. During exponential phases, spread seems unstoppable. During slow phases, containment appears successful. Amara's Law emerges from S-curve dynamics: exponential thinking fails during lag phases (underestimating long-term impact) and during plateau phases (overestimating continued exponential growth). We're optimized for linear change; biology proceeds in sigmoids. The lag phase prepares mechanisms invisibly. The exponential phase deploys them explosively through multiplicative growth—each generation doubling the previous, compounding until constraints emerge. The plateau phase reveals limits invisible during growth. Every biological invasion, epidemic, and growth process follows this pattern. We consistently misjudge all three phases.