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If you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future).

Benoit Mandelbrot

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Nature Past Science

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In fact, I barely missed being number one in France in both schools. In particular I did very well in mathematical problems.
BENOIT MANDELBROT

Country Numbers Problem School
$Benoit Mandelbrot Quote - Both chaos theory and fractal have had contacts in the past when they are both impossible to develop and in a certain sense not ready to be developed.$

Both chaos theory and fractal have had contacts in the past when they are both impossible to develop and in a certain sense not ready to be developed.
BENOIT MANDELBROT

Chaos Impossible Past
Self-similarity is a dull subject because you are used to very familiar shapes. But that is not the case. Now many shapes which are self-similar again, the same seen from close by and far away, and which are far from being straight or plane or solid.
BENOIT MANDELBROT

Case Dull Self Shape Shapes
An extraordinary amount of arrogance is present in any claim of having been the first in inventing something.
BENOIT MANDELBROT

Arrogance Claims Firsts
$Benoit Mandelbrot Quote - I spent half my life, roughly speaking, doing the study of nature in many aspects and half of my life studying completely artificial shapes. And the two are extraordinarily close; in one way both are fractal.$

I spent half my life, roughly speaking, doing the study of nature in many aspects and half of my life studying completely artificial shapes. And the two are extraordinarily close; in one way both are fractal.
BENOIT MANDELBROT

Half Shapes Two
There are very complex shapes which would be the same from close by and far away.
BENOIT MANDELBROT

Complex Far Away Shapes
I didn’t feel comfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of everything and explore the world.
BENOIT MANDELBROT

Firsts Littles Mathematician Pure World
$Benoit Mandelbrot Quote - The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.$

The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.
BENOIT MANDELBROT

Chaos Shapes Strong
One couldn’t even measure roughness. So, by luck, and by reward for persistence, I did found the theory of roughness, which certainly I didn’t expect and expecting to found one would have been pure madness.
BENOIT MANDELBROT

Luck Persistence Reward
Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside because they were too complicated.
BENOIT MANDELBROT

Circles Lines Shapes
Pictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion.
BENOIT MANDELBROT

Fashion Happen Mathematics Strong
Think not of what you see, but what it took to produce what you see.
BENOIT MANDELBROT

Produce See Thinking Took
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.
BENOIT MANDELBROT

Lying Mountain Nature Science Tree
Engineering is too important to wait for science.
BENOIT MANDELBROT

Engineering Important Waiting
Round about the accredited and orderly facts of every science there ever floats a sort of dustcloud of exceptional observations, of occurrences minute and irregular and seldom met with, which it always proves more easy to ignore than to attend to.
BENOIT MANDELBROT

Facts Observation Order Science
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 MANDELBROT

Circles Clouds Mountain

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