Academics From France

"My efforts over the years had been successful to the extent, to take an example, that fractals made many mathematicians learn a lot about physics, biology, and economics. Unfortunately, most were beginning to feel they had learned enough to last for the rest of their lives. They remained mathematicians, had been changed by considering the new problems I raised, but largely went their own way."

"My ambition was not to create a new field, but I would have welcomed a permanent group of people having interests close to mine and therefore breaking the disastrous tendency towards increasingly well-defined fields. Unfortunately, I failed on this essential point, very badly. Order doesn't come by itself."

"There is a saying that every nice piece of work needs the right person in the right place at the right time. For much of my life, however, there was no place where the things I wanted to investigate were of interest to anyone. So I spent much of my life as an outsider, moving from field to field, and back again, according to circumstances. Now that I near 80, write my memoirs, and look back, I realize with wistful pleasure that on many occasions I was 10, 20, 40, even 50 years "ahead of my time."

"The Mandelbrot set covers a small space yet carries a large number of different implications. Is it a fitting epitaph? Absolutely."

"My work is more varied than at any other point in my life. I am still carrying out research in pure mathematics. And I am working on an idea that I had several years ago on negative dimensions. … Negative dimensions are a way of measuring how empty something is. In mathematics, only one set is called empty. It contains nothing whatsoever. But I argued that some sets are emptier than others in a certain useful way. It is an idea that almost everyone greets with great suspicion, thinking I've gone soft in the brain in my old age. Then I explain it and people realise it is obvious. Now I'm developing the idea fully with a colleague. I have high hopes that once we write it down properly and give a few lectures about it at suitable places that negative dimensions will become standard in mathematics."

"In a different era, I would have called myself a natural philosopher. All my life, I have enjoyed the reputation of being someone who disrupted prevailing ideas. Now that I'm in my 80th year, I can play on my age and provoke people even more."

"There is a problem that is specific to financial markets. In most fields of research, when someone makes an important finding, they publish it. In the case of prices, they set up a firm and sell advice about their discovery. If they can make money from it, they will. So the research into market dynamics is a closed field."

"The most important thing I have done is to combine something esoteric with a practical issue that affects many people. In this spirit, the stock market is one of the most attractive things imaginable. Stock-market data is abundant so I can check everything. Financial markets are very influential and I want to be part of this field now that it is maturing."

"What motivates me now are ideas I developed 10, 20 or 30 years ago, and the feeling that these ideas may be lost if I don't push them a little bit further."

"My life seemed to be a series of events and accidents. Yet when I look back I see a pattern."

"The Mandelbrot set is the modern development of a theory developed independently in 1918 by Gaston Julia and Pierre Fatou. Julia wrote an enormous book — several hundred pages long — and was very hostile to his rival Fatou. That killed the subject for 60 years because nobody had a clue how to go beyond them. My uncle didn't know either, but he said it was the most beautiful problem imaginable and that it was a shame to neglect it. He insisted that it was important to learn Julia's work and he pushed me hard to understand how equations behave when you iterate them rather than solve them. At first, I couldn't find anything to say. But later, I decided a computer could take over where Julia had stopped 60 years previously."

"There is no single rule that governs the use of geometry. I don't think that one exists."

"There is nothing more to this than a simple iterative formula. It is so simple that most children can program their home computers to produce the Mandelbrot set. … Its astounding complication was completely out of proportion with what I was expecting. Here is the curious thing: the first night I saw the set, it was just wild. The second night, I became used to it. After a few nights, I became familiar with it. It was as if somehow I had seen it before. Of course I hadn't. No one had seen it. No one had described it. The fact that a certain aspect of its mathematical nature remains mysterious, despite hundreds of brilliant people working on it, is the icing on the cake to me."

"I always felt that science as the preserve of people from Oxbridge or Ivy League universities — and not for the common mortal — was a very bad idea."

"Many creative minds overrate their most baroque works, and underrate the simple ones."

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

"A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension."

"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."

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

"Engineering is too important to wait for science."

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

"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."

"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 subtle disciplines"

"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.""

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

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

"How Long Is the Coast of Britain?"

"Myth does not set out to give lessons in natural science any more than in morals or sociology."

"Myth therefore seems to choose history, rather than be chosen by it."

"So-called "realist" photography does not capture the "what is." Instead, it is preoccupied with what should not be, like the reality of suffering for example."

"There are only a few images that are not forced to provide meaning, or have to go through the filter of a specific idea."

"To challenge and to cope with this paradoxical state of things, we need a paradoxical way of thinking; since the world drifts into delirium, we must adopt a delirious point of view. We must no longer assume any principle of truth, of causality, or any discursive norm. Instead, we must grant both the poetic singularity of events and the radical uncertainty of events. It is not easy. We usually think that holding to the protocols of experimentation and verification is the most difficult thing. But in fact the most difficult thing is to renounce the truth and the possibility of verification, to remain as long as possible on the enigmatic, ambivalent, and reversible side of thought."

"The world is not dialectical -- it is sworn to extremes, not to equilibrium, sworn to radical antagonism, not to reconciliation or synthesis. This is also the principle of evil."

"The Violence of the Image European Graduate School."

"This realistic image, however, does not catch at all what really is, but what should not be - death and misery - what should not exist, from our moral and humanistic point of view. And at the same time making an aesthetic and commercial, perfectly immoral use and abuse of this misery. Images that actually testify, behind their pretended "objectivity", of a deep denial of the real, and of an equal denial of the image - assigned to present what does not even want to be represented, assigned to the rape of the real by burglary."

"Particularly in the case of all professional of press-images which testify of the real events. In making reality, even the most violent, emerge to the visible, it makes the real substance disappear. It is like the Myth of Eurydice : when Orpheus turns around to look at her, she vanishes and returns to hell. That is why, the more exponential the marketing of images is growing the more fantastically grows the indifference towards the real world. Finally, the real world becomes a useless function, a collection of phantom shapes and ghost events. We are not far from the silhouettes on the walls of the cave of Plato."

"Today's terrorism is not the product of a traditional history of anarchism, nihilism, or fanaticism. It is instead the contemporary partner of globalization."

"The simulacrum now hides, not the truth, but the fact that there is none, that is to say, the continuation of Nothingness."

"Not only does reality resist those who still criticize it, but it also abandons those who defend it. Maybe it is a way for reality to get its revenge from those who claim to believe in it for the sole purpose of eventually transforming it: sending back its supporters to their own desires."

"If the thought enunciates an object as a truth, it is only as a challenge to this object's own self-fulfillment."

"One may dream of a culture where everyone bursts into laughter when someone says: this is true, this is real."

"We will never know if an advertisement or opinion poll has had a real influence on individual or collective wills, but we will never know either what would have happened if there had been no opinion poll or advertisement."

"Nothing is wholly obvious without becoming enigmatic. Reality itself is too obvious to be true."

"The end of history is, alas, also the end of the dustbins of history. There are no longer any dustbins for disposing of old ideologies, old regimes, old values. Where are we going to throw Marxism, which actually invented the dustbins of history? (Yet there is some justice here since the very people who invented them have fallen in.) Conclusion: if there are no more dustbins of history, this is because History itself has become a dustbin. It has become its own dustbin, just as the planet itself is becoming its own dustbin."

"For nothing can be greater than seduction itself, not even the order that destroys it."

"The apocalypse is finished, today it is the precession of the neutral, of forms of the neutral and of indifference. I will leave it to be considered whether there can be a romanticism, an aesthetic of the neutral therein. I don't think so—all that remains, is the fascination for desertlike and indifferent forms, for the very operation of the system that annihilates us. Now, fascination (in contrast to seduction, which was attached to appearances, and to dialectical reason, which was attached to meaning) is a nihilistic passion par excellence, it is the passion proper to the mode of disappearance. We are fascinated by all forms of disappearance, of our disappearance. Melancholic and fascinated, such is our general situation in an era of involuntary transparency. I am a nihilist. I observe, I accept, I assume the immense process of the destruction of appearances (and of the seduction of appearances) in the service of meaning (representation, history, criticism, etc.) that is the fundamental fact of the nineteenth century."

"The "hard law of value," the "law set in stone"—when it abandons us, what sadness, what panic! This is why there are still good days left to fascist and authoritarian methods, because they revive something of the violence necessary to life—whether suffered or inflicted. The violence of ritual, the violence of work, the violence of knowledge, the violence of blood, the violence of power and of the political is good! It is clear, luminous, the relations of force, contradictions, exploitation, repression! This is lacking today, and the need for it makes itself felt."

"Those who used to sacrifice animals did not take them for beasts. And even the Middle Ages, which condemned and punished them in due form, was in this way much closer to them than we are, we who are filled with horror at this practice. They held them to be guilty: which was a way of honoring them. We take them for nothing, and it is on this basis that we are "human" with them. We no longer sacrifice them, we no longer punish them, and we are proud of it, but it is simply that we have domesticated them, worse: that we have made of them a racially inferior world, no longer even worthy of our justice, but only of our affection and social charity, no longer worthy of punishment and of death, but only of experimentation and extermination like meat from the butchery."

"Whatever it may be, animals have always had, until our era, a divine or sacrificial nobility that all mythologies recount. Even murder by hunting is still a symbolic relation, as opposed to an experimental dissection. Even domestication is still a symbolic relation, as opposed to industrial breeding. One only has to look at the status of animals in peasant society. And the status of domestication, which presupposes land, a clan, a system of parentage of which the animals are a part, must not be confused with the status of the domestic pet—the only type of animals that are left to us outside reserves and breeding stations—dogs, cats, birds, hamsters, all packed together in the affection of their master. The trajectory animals have followed, from divine sacrifice to dog cemeteries with atmospheric music, from sacred defiance to ecological sentimentality, speaks loudly enough of the vulgarization of the status of man himself."

"Once animals had a more sacred, more divine character than men. There is not even a reign of the "human" in primitive societies, and for a long time the animal order has been the order of reference. Only the animal is worth being sacrificed, as a god, the sacrifice of man only comes afterward, according to a degraded order. Men qualify only by their affiliation to the animal: the Bororos "are" macaws."