Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
Interpretation
This quote highlights the complexity and irregularity of natural forms contrary to simplistic geometric shapes.
Benoit Mandelbrot emphasizes the idea that the natural world is far more intricate than the simplistic geometric forms we often attribute to it. Instead of being perfectly smooth and uniform, nature exhibits a diverse range of irregularities and complexities that are crucial to its beauty and function, which is captured in the study of fractals.
In practice
In a presentation on environmental science, one might quote this to emphasize the complexity of ecosystems.
The existence of these patterns [fractals] challenges us to study forms that Euclid leaves aside as being formless, to investigate the morphology of the amorphous. Mathematicians have disdained this challenge, however, and have increasingly chosen to flee from nature by devising theories unrelated to anything we can see or feel.
Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.
Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline or a tree.
We live in a time when the words impossible and unsolvable are no longer part of the scientific community's vocabulary. Each day we move closer to trials that will not just minimize the symptoms of disease and injury but eliminate them.
Now I know what the atom looks like.
I believe that the extraordinary should be pursued. But extraordinary claims require extraordinary evidence.
All policies should be guided by science, not just whose voice is the loudest.
Nearly all inventions are not recognised for their positive side either when they're made. So, for example, scientists didn't go out to design a CD machine: they designed a laser. But we got all sorts of things from a laser which we never remotely imagined, and we're still finding things for a laser to do.
That the fundamental aspects of heredity should have turned out to be so extraordinarily simple supports us in the hope that nature may, after all, be entirely approachable. Her much-advertised inscrutability has once more been found to be an illusion due to our ignorance. This is encouraging, for, if the world in which we live were as complicated as some of our friends would have us believe we might well despair that biology could ever become an exact science.
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