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.
It is a right, yes a duty, to search in cautious manner for the numbers, sizes, and weights, the norms for everything [God] has created. For He himself has let man take part in the knowledge of these things ... For these secrets are not of the kind whose research should be forbidden; rather they are set before our eyes like a mirror so that by examining them we observe to some extent the goodness and wisdom of the Creator.
I'm on a crusade to get movie directors to get their science right because, more often than they believe, the science is more extraordinary than anything they can invent.
Science is simply common sense at its best.
For far more marvelous is the truth than any artists of the past imagined it. Why do the poets of the present not speak of it? What men are poets who can speak of Jupiter if he were a man, but if he is an immense spinning sphere of methane and ammonia must be silent?
Everyone in the astronaut program has a degree in a science field. The crew are the ones who do the experiments, help to design some of the experiments that come from other primary researchers. So it becomes very important that you have a science background.
I am mindful that scientific achievement is rooted in the past, is cultivated to full stature by many contemporaries and flourishes only in favorable environment. No individual is alone responsible for a single stepping stone along the path of progress, and where the path is smooth progress is most rapid. In my own work this has been particularly true.
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