Top 94 Quotes & Sayings by Benoit Mandelbrot
Explore popular quotes and sayings by a French mathematician Benoit Mandelbrot.
Last updated on September 11, 2024.
Father was bold, and Mother was cautious. They never shouted at each other but argued constantly about strategy, and they taught me very early that before taking big risks, one must carefully figure the odds.
Now that I near 80, I realize with wistful pleasure that on many occasions I was 10, 20, 40, even 50 years ahead of my time.
When I first began studying prices, it wasn't a topic that mathematicians were working on. Purely by accident, I saw a set of data on price changes presented in a lecture and realized they behaved similarly to the geometric models I was already studying.
Where do I really belong? I avoid saying everywhere - which switches all too easily to nowhere. Instead, when pressed, I call myself a fractalist.
Smooth shapes are very rare in the wild but extremely important in the ivory tower and the factory.
The techniques I developed for studying turbulence, like weather, also apply to the stock market.
Most economists, when modeling market behavior, tend to sweep major fluctuations under the rug and assume they are anomalies. What I have found is that major rises and falls in prices are actually inevitable.
Order doesn't come by itself.
Most were beginning to feel they had learned enough to last for the rest of their lives. They remained mathematicians, but largely went their own way.
Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics.
I don't seek power and do not run around.
A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don't get something smooth, but irregularities at a smaller scale.
I was in an industrial laboratory because academia found me unsuitable.
My fate has been that what I undertook was fully understood only after the fact.
Until a few years ago, the topics in my Ph.D. were unfashionable, but they are very popular today.
An exquisitely complex shape now known as the Mandlebrot set has been called the most complex object in mathematics.
Although computer memory is no longer expensive, there's always a finite size buffer somewhere. When a big piece of news arrives, everybody sends a message to everybody else, and the buffer fills.
Both parents worshiped individual achievement, but because of the Depression and the war, they never achieved what they wanted and deserved. So their ambition and high expectations were transferred to me.
When the weather changes, nobody believes the laws of physics have changed. Similarly, I don't believe that when the stock market goes into terrible gyrations its rules have changed.
There is a saying that every nice piece of work needs the right person in the right place at the right time.
There's nothing really connecting the behavior of the Nile, metallurgy, and the behavior of prices except that I had the mathematical tools to explain them.
Nobody will deny that there is at least some roughness everywhere.
For much of my life there was no place where the things I wanted to investigate were of interest to anyone.
An extraordinary amount of arrogance is present in any claim of having been the first in inventing something.
There is a joke that your hammer will always find nails to hit. I find that perfectly acceptable.
If you look at coastlines, if you look at that them from far away, from an airplane, well, you don't see details, you see a certain complication. When you come closer, the complication becomes more local, but again continues. And come closer and closer and closer, the coastline becomes longer and longer and longer because it has more detail entering in.
Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics
Regular geometry, the geometry of Euclid, is concerned with shapes which are smooth, except perhaps for corners and lines, special lines which are singularities, but some shapes in nature are so complicated that they are equally complicated at the big scale and come closer and closer and they don't become any less complicated.
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.
A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales...
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.
Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.
Beautiful, damn hard, increasingly useful. That's fractals.
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.
Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
The Mandelbrot set is the most complex mathematical object known to mankind.
If you look at a shape like a straight line, what's remarkable is that if you look at a straight line from close by, from far away, it is the same; it is a straight line.
Engineering is too important to wait for science.
The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.
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.
I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid - a term used in this work to denote all of standard geometry - Nature exhibits not simply a higher degree but an altogether different level of complexity ... The existence of these patterns challenges us to study these forms that Euclid leaves aside as being "formless," to investigate the morphology of the "amorphous."
Think not of what you see, but what it took to produce what you see.
Nobody will deny that there is at least some roughness everywhere
Many painters had a clear idea of what fractals are. Take a French classic painter named Poussin. Now, he painted beautiful landscapes, completely artificial ones, imaginary landscapes. And how did he choose them? Well, he had the balance of trees, of lawns, of houses in the distance. He had a balance of small objects, big objects, big trees in front and his balance of objects at every scale is what gives to Poussin a special feeling.
There is a joke that your hammer will always find nails to hit. I find that perfectly acceptable
The most complex object in mathematics, the Mandelbrot Set ... is so complex as to be uncontrollable by mankind and describable as 'chaos'.
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.
My life has been extremely complicated. Not by choice at the beginning at all, but later on, I had become used to complication and went on accepting things that other people would have found too difficult to accept.
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.
There are very complex shapes which would be the same from close by and far away.
A fractal is a way of seeing infinity.
Asking the right questions is as important as answering them
A formula can be very simple, and create a universe of bottomless complexity.
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.
The most important thing I have done is to combine something esoteric with a practical issue that affects many people.
I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit.
For most of my life, one of the persons most baffled by my own work was myself.
Bottomless wonders spring from simple rules, which are repeated without end.
The straight line has a property of self-similarity. Each piece of the straight line is the same as the whole line when used to a big or small extent.
I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.
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