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.
...But there's always suffering, Pudge. Homework or malaria or having a boyfriend who lives far away when there's a good-looking boy lying next to you. Suffering is universal. It's the one thing Buddhists, Christians, and Muslims are all worried about.
I went inside my heart to see how it was. Something there makes me hear the whole world weeping.
somehow one must love the world without being worldly.
Absolute truth is not dependent upon public opinion or popularity. Now what is this truth? It is His gospel. It is the gospel of Jesus Christ.
Since man cannot live without miracles, he will provide himself with miracles of his own making. He will believe in witchcraft and sorcery, even though he may otherwise be a heretic, an atheist, and a rebel.
Guilt is perhaps the most painful companion of death.
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