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.
Benoit MandelbrotRead
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.
Interpretation
What this quote means
The quote emphasizes the importance of studying complex natural patterns that traditional mathematics neglects.
Benoit Mandelbrot highlights the necessity of exploring unconventional forms in nature, specifically fractals, which defy classical geometric definitions provided by Euclid. He criticizes mathematicians for ignoring these natural phenomena in favor of abstract theories that disconnect from observable reality, advocating for a deeper understanding of the intricate structures that make up our world.
Themes
FractalsMathematicsNaturePatternsEuclid
In practice
Example use cases
This quote could be used in a discussion about the relevance of studying fractals in art and nature.
More from Benoit Mandelbrot
All quotes βFractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.
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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.
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