Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.
Interpretation
Fractal geometry provides us with a new perspective on understanding complex patterns in nature and mathematics.
Benoit Mandelbrot's quote emphasizes that fractal geometry goes beyond a mere mathematical concept; it serves as a lens through which everyone can observe and interpret the world around them in an innovative way. This branch of mathematics reveals the intricate and often hidden structures that exist in nature, encouraging people to appreciate complexity and patterns that are typically unseen in traditional geometric frameworks.
In practice
In a mathematics class discussing the applications of fractal geometry in nature.
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.
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.
The missing link in cosmology is the nature of dark matter and dark energy.
There must be no barriers for freedom of inquiry... There is no place for dogma in science. The scientist is free, and must be free to ask any question, to doubt any assertion, to seek for any evidence, to correct any errors.
I think we're just scratching the surface. One of the most exciting aspects of 23andMe is that we're enabling you to watch a revolution unfold live during your lifetime, and I think that the decoding of the genome, in my opinion, is the most fascinating discovery of our lifetime, and you get to be part of it.
I don't care much for equations myself. This is partly because it is difficult for me to write them down, but mainly because I don't have an intuitive feeling for equations.
If ever there was a slamming of the door in the face of constructive investigation, it is the word miracle. To a medieval peasant, a radio would have seemed like a miracle.
Iβve spent something like 17 years working on a theory for which there is essentially no direct experimental support.
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