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.
There is no scientific reason to think that we, even with space travel, are going to survive as a species for ever, certainly not by biting off the hand that feeds us, which is exactly what we are doing.
If we examine the accomplishments of man in his most advanced endeavors, in theory and in practice, we find that the cell has done all this long before him, with greater resourcefulness and much greater efficiency.
The man who discovers a new scientific truth has previously had to smash to atoms almost everything he had learnt, and arrives at the new truth with hands blood stained from the slaughter of a thousand platitudes.
It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.
It is ... a sign of the times-though our brothers of physics and chemistry may smile to hear me say so-that biology is now a science in which theories can be devised: theories which lead to predictions and predictions which sometimes turn out to be correct. These facts confirm me in a belief I hold most passionately-that biology is the heir of all the sciences.
In the distant future I see open fields for far more important researches. Psychology will be based on a new foundation, that of the necessary acquirement of each mental power and capacity by gradation. Light will be thrown on the origin of man and his history.
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