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.
The impression sometimes created among the public is that scientists are working away in their labs, and maybe they're not always thinking about the implications of their work. But we are.
The time has come when scientific truth must cease to be the property of the few, when it must be woven into the common life of the world.
Certainly I see the scientific view of the world as incompatible with religion, but that is not what is interesting about it. It is also incompatible with magic, but that also is not worth stressing. What is interesting about the scientific world view is that it is true, inspiring, remarkable and that it unites a whole lot of phenomena under a single heading.
The slow rejection of the foreign skin grafts fascinated me. How could the host distinguish another person's skin from his own?
I'm convinced that sending people to Mars is so expensive that if you go once and bring the people back and then go again and bring the people back, we're eventually going to run out of money. But what if we send people the first time and they don't come back? What if they stay there?
I am disappointed because nobody is talking about food and agriculture. They're talking about the diets of children, but they're talking about Band-Aids. We're not seeing a vision.
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