Adrian Bejan | Hierarchy in Movement on Area, from Design in Nature

In this video, Adrian Bejan explains the evolution of airplanes as part of the movement of people on Earth today, and uses that topic to lead into a concluding section on the design of society and the words used to describe that design. He reviews a simple airplane model with a fuel tank and an engine, and emphasizes that movement is the product of the stuff being moved and the distance, which is what costs money. He then shifts to movers on an elemental area, drawn as a rectangle, with one big mover traveling a long distance and many smaller movers traveling transversely, and he focuses on keeping the movement going while burning less fuel. He introduces a two-part model for each mover as an empty structure plus a motor, connects fuel consumption to work, and shows how economies of scale appear as the size of what is moved increases. From minimizing fuel use across the territory, he argues that movement becomes hierarchical, with many small moving short and few big moving long, and he ends by linking hierarchy in movement and fuel consumption to hierarchy in wealth on the same territory.

• He revisits the idea that big airplane, big engine, and big fuel load scale together, so one drawing can be magnified or reduced to represent different sizes. This sets up the idea that the same kind of correlation can be tried again on trucks on the highway and other groups.

• He defines movement as stuff times distance and treats that product as the real cost, because moving bigger things and moving farther are both more expensive. This leads him to treat fuel consumption as the key objective in economics, a very old attitude.

• He builds a territory model with two dimensions and a total mass composed of one big mover and a number of small movers, then identifies degrees of freedom such as the rectangle's shape, the ratio of vehicle sizes, and the number of small movers. He uses a simple plan to determine these, so the same movement can continue with less fuel.

• He models each mover as structure plus motor and argues that the trade-off in fuel requirement occurs when those two parts are of the same order of magnitude. From there, he connects the result to economies of scale, in which fuel cost per unit of mass moved decreases as the mass moved increases.

• He shows that the smaller movers should travel shorter distances while the bigger mover travels longer distances, and he calls the resulting pattern hierarchy. He then compares different drawings of how small movers join into a big mover, like a trunk that collects flow, and links this hierarchy in movement and fuel consumption to a hierarchy in wealth.

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