Benoit Mandelbrot Quotations

My fate has been that what I undertook was fully understood only after the fact.

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

There is a saying that every nice piece of work needs the right person in the right place at the right time.

The techniques I developed for studying turbulence, like weather, also apply to the stock market

Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics

Smooth shapes are very rare in the wild but extremely important in the ivory tower and the factory

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.

Nobody will deny that there is at least some roughness everywhere

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 joke that your hammer will always find nails to hit. I find that perfectly acceptable

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

I don't seek power and do not run around

I was in an industrial laboratory because academia found me unsuitable

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

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.

One of my conjectures was solved in six months, a second in five years, a third in 10. But the basic conjecture remains-the Mandelbrot Set.

I spent my time very nicely in many ways, but not fully satisfactory. Then I became Professor in France, but realized that I was not - for the job that I should spend my life in.

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."

Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.

The extraordinary fact is that the first idea I had which motivated me, that worked, is conjecture, a mathematical idea which may or may not be true. And that idea is still unproven. It is the foundation, what started me and what everybody failed to **** prove has so far defeated the greatest efforts by experts to be proven.

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.

Order doesn't come by itself.

A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales.

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).

I was asking questions which nobody else had asked before, because nobody else had actually looked at certain structures. Therefore, as I will tell, the advent of the computer, not as a computer but as a drawing machine, was for me a major event in my life. That's why I was motivated to participate in the birth of computer graphics, because for me computer graphics was a way of extending my hand, extending it and being able to draw things which my hand by itself, and the hands of nobody else before, would not have been able to represent.

Some mathematicians didn't even perceive of the possibility of a picture being helpful. To the contrary, I went into an orgy of looking at pictures by the hundreds; the machines became a little bit better.

There are very complex shapes which would be the same from close by and far away.

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.

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.

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.

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.

I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.

Everybody in mathematics had given up for 100 years or 200 years the idea that you could from pictures, from looking at pictures, find new ideas. That was the case long ago in the Middle Ages, in the Renaissance, in later periods, but then mathematicians had become very abstract.

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

One of the high points of my life was when I suddenly realized that this dream I had in my late adolescence of combining pure mathematics, very pure mathematics with very hard things which had been long a nuisance to scientists and to engineers, that this combination was possible and I put together this new geometry of nature, the fractal geometry of nature.

When people ask me what's my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.

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.

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.

I've been a professor of mathematics at Harvard and at Yale. At Yale for a long time. But I'm not a mathematician only. I'm a professor of physics, of economics, a long list. Each element of this list is normal. The combination of these elements is very rare at best.

If one takes the kinds of risks which I took, which are colossal, but taking risks, I was rewarded by being able to contribute in a very substantial fashion to a variety of fields. I was able to reawaken and solve some very old problems.

I had many books and I had dreams of all kinds. Dreams in which were in a certain sense, how to say, easy to make because the near future was always extremely threatening.

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.

In mathematics and science definition are simple, but bare-bones. Until you get to a problem which you understand it takes hundreds and hundreds of pages and years and years of learning.

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.

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.

It was astonishing when at one point, I got the idea of how to make artifical clouds with a collaborator, we had pictures made which were theoretically completely artificial pictures based upon that one very simple idea. And this picture everybody views as being clouds.

Humanity has known for a long time what fractals are. It is a very strange situation in which an idea which each time I look at all documents have deeper and deeper roots, never (how to say it), jelled.

The beauty of what I happened by extraordinary chance to put together is that nobody would have believed that this is possible, and certainly I didn't expect that it was possible. I just moved from step to step to step.

Bottomless wonders spring from simple rules, which are repeated without end.

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. 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... Nature exhibits not simply a higher degree but an altogether different level of complexity.

Think not of what you see, but what it took to produce what you see.

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 most important thing I have done is to combine something esoteric with a practical issue that affects many people.

A formula can be very simple, and create a universe of bottomless complexity.

A fractal is a way of seeing infinity.

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.

Being a language, mathematics may be used not only to inform but also, among other things, to seduce.

The most complex object in mathematics, the Mandelbrot Set ... is so complex as to be uncontrollable by mankind and describable as 'chaos'.

It was a very big gamble. I lost my job in France, I received a job in which was extremely uncertain, how long would IBM be interested in research, but the gamble was taken and very shortly afterwards, I had this extraordinary fortune of stopping at Harvard to do a lecture and learning about the price variation in just the right way.

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 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 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.

Engineering is too important to wait for science.

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.

Beautiful, damn hard, increasingly useful. That's fractals.

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.

Unfortunately, the world has not been designed for the convenience of mathematicians.

For most of my life, one of the persons most baffled by my own work was myself.

I had very, very little training in taking an exam to determine a scientist's life in France.

Science would be ruined if (like sports) it were to put competition above everything else, and if it were to clarify the rules of competition by withdrawing entirely into narrowly defined specialties. The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.

Asking the right questions is as important as answering them

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

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.

If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.

The Mandelbrot set is the most complex mathematical object known to mankind.

I didn't want to become a pure mathematician, as a matter of fact, my uncle was one, so I knew what the pure mathematician was and I did not want to be a pure - I wanted to do something different.

Until a few years ago, the topics in my Ph.D. were unfashionable, but they are very popular today.