Scaling and Differential Shrinking

For example, how fast an organism takes oxygen from the air, digests and absorbs food, and loses or gains heat are proportional to the areas of the lung, gut, and body surfaces, respectively. These combined relationships mean that rates of acquisitions or losses are proportional to the masses or volumes of the body. They are also proportional to how the different functions connect. Or at any given mass, size is limited, because as skeletons decrease their masses accommodating other functions within a fixed volume, there comes a point when the skeleton becomes too flimsy and cuticles too thin to support the body. Skeletons are usually no more than ten percent of a system's mass.

Because the geometries underlying different functions change at different rates as an object shrinks, a change in the size of the object alone implies that functions related to size must also change, but at varying rates. If an organism or device is to remain functional as it shrinks, either these relationships must change, or the shape must change.

Size changes compel adjustments on many levels of organization simultaneously. Molecular forces, such as cohesion, become more important as mass decreases; flies walk upside down on ceilings because the force of gravity on a fly is less than cohesive forces holding the fly on the ceiling. Or to quote from Thompson's On Growth and Form: 'A man coming wet from his bath carries a few ounces of water and is perhaps 1% heavier than before; but a wet fly weighs twice as much as a dry one and becomes a helpless thing.' (Ref: Thompson, 1942).

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