Adrian Bejan | Logistics S Curve, from Design in Nature
In this video, Adrian Bejan explains the logistics S-curve, the universal shape that describes how almost anything spreads or is collected over time. He traces the word “logistics” back to military engineering rather than philosophy, argues that the “exponential growth” people invoke for viral phenomena is actually the wrong word, and then shows how a simple two-dimensional conduction model reproduces the S-curve through two stages he calls invasion and consolidation. He ties the whole idea to the German blitzkrieg through France and even to rainwater spreading across the ground.
Where “logistics” comes from. Bejan opens with Napoleon, who understood that an army “marches on its belly” and needs food and lodging to keep moving. That need for lodging from stop to stop is the origin of the word logistics, meaning military engineering, not logic or philosophy.
The S-curve is universal. Anything that spreads or is collected grows slowly, then fast, then slowly again, tracing the same S shape that you cannot defeat. Bejan’s recent contribution was not just to observe this curve but to predict it.
“Exponential” is a misnomer. People call the steep early part of viral growth exponential, but a true exponential curve starts at minus infinity and keeps climbing forever. Since nothing in nature starts before the Big Bang, Bejan says that calling real growth exponential forgets your high school mathematics.
Invasion then consolidation. In his model, a hot blade first cuts long and fast into a cooler square, then grows across it like a finger, producing the convex early rise. Once it reaches the far wall, the heat spreads sideways more slowly to fill the rest, the concave tail, which are the two phases he calls invasion and consolidation.
A wartime newsreel made it click. The idea came from a Hollywood newsreel of Germany’s blitzkrieg into France, which bypassed France’s fortified eastern frontier by marching through Belgium. Tanks raced down the highway to Paris while trucks behind them spread sideways to protect the channel, an invasion followed by consolidation, exactly as in his model.
The same pattern is everywhere. Rainwater falling on the ground first runs as a rivulet, then diffuses laterally and turns the patch into mud or swamp. The S-curve, Bejan argues, governs everything that fills a territory in time.
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