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.
Interpretation
Geometry is often seen as a rigid discipline that struggles to capture the complexity of natural forms.
In this quote, Benoit Mandelbrot highlights the limitations of geometry as a mathematical tool that can accurately depict the irregular and intricate shapes found in nature. He suggests that while geometry provides valuable structural insights, its inherent abstraction fails to encapsulate the fluidity and variability present in organic forms such as clouds and trees.
In practice
In a lecture on the limitations of mathematical models in describing natural phenomena.
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.
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.
Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.
We must, however, acknowledge, as it seems to me, that man with all his noble qualities... still bears in his bodily frame the indelible stamp of his lowly origin.
The minds of men are mirrors to one another, not only because they reflect each other's emotions, but also because those rays of passions, sentiments and opinions may be often reverberated, and may decay away by insensible degrees.
By my existence I am nothing more than an empty place, an outline,that is reserved within being in general. Given with it, though, is the duty to fill in this empty place. That is my life.
Surrounded, detached, in measureless oceans of space.
To be mad is to feel with excruciating intensity the sadness and joy of a time which has not arrived or has already been.
Neither of my parents went to church, but they did everything that you needed to do to be Christian. That's something a Quaker would call an intimation of the divine.
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