In the realm of mathematics, perfection abounds. Lines stretch straight to infinity, planes are flawlessly flat, and spheres are impeccably round. The real world, however, is almost always irregular–the jagged spear of a lightning bolt, the rough face of a broken rock, and the ragged profile of a mountain range are just a few examples. Although people have always been surrounded by texture, until recently they could not describe it in anything other than qualitative terms such as smooth or rugged or lumpy. Long after scientists developed ways to measure physical properties such as temperature, weight, and time, the techniques needed to quantify roughness eluded them.
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