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.
Most political leaders acquire their position by causing large numbers of people to believe that these leaders are actuated by altruistic desires
I feel my heart break to see a nation ripped apart by it's own greatest strength - it's diversity.
The past is only an unreliable memory held in the present. The future is only a projection of our present conceptions. The present itself vanishes as soon as we try to grasp it. So why bother with attempting to establish an illusion of solid ground?
A blueprint for disaster in any society is when the elite are capable of insulating themselves.
People born in Puerto Rico are U.S. citizens - except for the teeny, tiny, mind-boggling fact that if you live in Puerto Rico, you are not allowed to cast a vote in the election for president. That tiny fact starts to get bigger when you realize that electing our own leaders is the whole reason that we have a country in the first place.
The tradition of nonviolence, optimism, concern for the individual, and unconditional compassion that developed in Tibet is the culmination of a slow inner revolution, a cool one, hard to see, that began 2,500 years ago with the Buddha's insight about the end of suffering. What I have learned from these people has forever changed my life, and I believe their culture contains an inner science particularly relevant to the difficult time in which we live.
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