A matter of scale

Late afternoon sun reflects from deeply incised bedrock. How large is this scene – are we looking at a canyon hundreds of feet deep, or instead at a small rivulet? The stream here is nearly one foot wide. You probably guessed that correctly, but how? The mind is adept at picking up on small cues that help us distinguish the relative and absolute magnitudes of large and small. Here, perhaps, the smoothness of the rock, or the curvature of the meniscus of water told you that this was a smaller scene. Many physical and biological processes operate on characteristic scales. For example, the viscous drag forces in water are far more important to a bacterium than to a whale, and the force of gravity is far more important to an elephant than to a mouse. In the latter case, a short look at the proportionately larger skeleton of the elephant illustrates that bones must become proportionately larger as an animal’s size increases. Scientists can use these scaling principles, and identifications of characteristic scales, to develop better models of the natural world – and of course help to disentangle photos like this one!

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