Academics From France

"The words of the world want to make sentences."

"Man is an imagining being."

""Memory is a field full of psychological ruins," wrote French philosopher Gaston Bachelard. For some that may be true, but memory is also a field of healing that has the capacity to restore the world, not only for the one person who recollects, but for cultures as well. When a person says "I remember," all things are possible."

"The repose of sleep refreshes only the body. It rarely sets the soul at rest. The repose of the night does not belong to us. It is not the possession of our being. Sleep opens within us an inn for phantoms. In the morning we must sweep out the shadows."

"Reverie is not a mind vacuum. It is rather the gift of an hour which knows the plenitude of the soul."

"The subconscious is ceaselessly murmuring, and it is by listening to these murmurs that one hears the truth."

"Childhood lasts all through life. It returns to animate broad sections of adult life.... Poets will help us to find this living childhood within us, this permanent, durable immobile world."

"I am a dreamer of words, of written words. I think I am reading; a word stops me. I leave the page. The syllables of the word begin to move around. Stressed accents begin to invert. The word abandons its meaning like an overload which is too heavy and prevents dreaming. Then words take on other meanings as if they had the right to be young. And the words wander away, looking in the nooks and crannies of vocabulary for new company, bad company."

"A word is a bud attempting to become a twig. How can one not dream while writing? It is the pen which dreams. The blank page gives the right to dream."

"Ideas are refined and multiplied in the commerce of minds. In their splendor, images effect a very simple communion of souls."

"Poetry is one of the destinies of speech.... One would say that the poetic image, in its newness, opens a future to language."

"The mollusk's motto would be: one must live to build one's house, and not build one's house to live in."

"Words … are little houses, each with its cellar and garret. Common sense lives on the ground floor, always ready to engage in ‘foreign commerce’ on the same level as the others, as the passers-by, who are never dreamers. To go upstairs in the word house is to withdraw step by step; while to go down to the cellar is to dream, it is losing oneself in the distant corridors of an obscure etymology, looking for treasures that cannot be found in words. To mount and descend in the words themselves—this is a poet’s life. To mount too high or descend too low is allowed in the case of poets, who bring earth and sky together."

"If I were asked to name the chief benefit of the house, I should say: the house shelters day-dreaming, the house protects the dreamer, the house allows one to dream in peace."

"The reflected world is the conquest of calm"

"True poetry is a function of awakening. It awakens us, but it must retain the memory of previous dreams."

"A man is a man to the extent that he is a superman. A man should be defined by the sum of those tendencies which impel him to surpass the human condition."

"Two seemingly incompatible conceptions can each represent an aspect of the truth … They may serve in turn to represent the facts without ever entering into direct conflict."

"It seems a little paradoxical to construct a configuration space with the coordinates of points which do not exist."

"Admettant que la particule possède une vibration interne qui permet de l'assimiler à une petite horloge, je supposais que cette horloge se déplaçait dans son onde de façon que sa vibration interne reste constamment en phase avec celle de l'onde : c'est le postulat de l'accord des phases."

"The actual state of our knowledge is always provisional and … there must be, beyond what is actually known, immense new regions to discover."

"The history of science shows that the progress of science has constantly been hampered by the tyrannical influence of certain conceptions that finally came to be considered as dogma. For this reason, it is proper to submit periodically to a very searching examination, principles that we have come to assume without any more discussion."

"The word fractal, once introduced, had an extraordinary integrating effect upon myself and upon many people around. Initially again it was simply a word to write a book about, but once a word exists one begins to try to define it, even though initially it was simply something very subjective and indicating my field. Now the main property of all fractals, put in very loose terms, is that each part — they're made of parts — each part is like the whole except it is smaller. After having coined this word I sorted my own research over a very long period of time and I realised that I had been doing almost nothing else in my life."

"If musical appreciation is a by-product of a more general pattern-processing propensity of the brain, then why are our senses heightened by pink noises? It is significant that the world around us is full of variations with 1/f spectra. Benoit Mandelbrot has pioneered the study of natural and computer-generated patterns that are scale-free. (He calls them fractals...) Mandelbrot draws attention to the fact that there is a pattern to the noise spectrum displayed by the human nervous system. At the extremities of the body... it tends to be of white-noise form; but, as one approaches closer to the central nervous system and the brain, these variations become 1/f-like. Our nervous system may act as a spectral filter to prevent the brain from being swamped with uninteresting white background noise about the world..."

"The thought that one unifying idea should continue forever is simply not realistic and therefore not to be hoped for, but I think that for quite a number of years still, perhaps if I am lucky to the end of my life, because I would hate to see that stop in my lifetime, those questions will become very active and still somewhat separate, as different branches of learning become accustomed to them. I cannot imagine that this idea would vanish, not because I am so proud of what I've been doing all my life, but because this is not an artificial thought coming from nowhere in no time and vanishing again rapidly in no time. It has in every one of its manifestations profound roots in the history of the various sciences and the various manners of human enterprise and those roots will not be broken. The continuity of these thoughts will continue, and if any substitute comes, if any other name comes, which is possible, the ideas will remain."

"The extraordinary surprise that my first pictures provoked is unlikely to be continued. Many people saw them fifteen years ago, ten years ago. Now children see it on their computers when the computers do nothing else. The surprise is not there. The shock of novelty is not there. Therefore the unity that the shock of novelty, surprise, provided to all these activities will not continue. People will know about fractals earlier and earlier, more and more progressively. I think that the best future to expect and perhaps also the best future to hope for, is that fractal ideas will remain either as a peripheral or as a central tool in very many fields."

"The next thing which surprised us very much, is that both for Julia sets and even more so for the Mandelbrot set, the complication was not, how to say, arbitrary, and almost everybody found the impression that these shapes were hauntingly beautiful. These shapes resulted from the most ridiculous transformation, z2+c, taken seriously, respectfully and visually. And people thought at first that they were totally wild, totally extraterrestrial, but then after a very short time, they came back and said, "You know, I think they remind me of something. I think they're natural. I think they are like perhaps nightmares or dreams, but they're natural." And this combination of being so new, because literally when we saw them nobody had seen them before, and being the next day so familiar, is still to me extraordinarily baffling."

"I think it's very important to have both cartoons and more realistic structures. The cartoons have the power of representing the essential very often, but have this intrinsic weakness of being in a certain sense predictable. Once you look at the Sierpinski triangle for a very long time you see more consequences of the construction, but they are rather short consequences, they don't require a very long sequence of thinking. In a certain sense, the most surprising, the richest sciences are those in which we start from simple rules and then go on to very, very long trains of consequences and very long trains of consequences, which you are still predicting correctly."

"Britain for a long time had a reflection of its class structure which meant that people like, well, J. B. S. Haldane who was the nephew of Lord Haldane, or Bertrand Russell who became Lord Russell, could do what they pleased, and it's interesting to think that Bertrand Russell never had a job, he never had to compete for a job. Haldane had four or five different jobs in his life, totally different. He probably could have — if he had been bothered — have just abandoned his job and went on to live otherwise. … But this no longer exists. IBM no longer exists. I don't see a place now where somebody like myself who combined, let's say, unusual gifts and unusual tastes and, who everybody said has promise, was certainly a misfit of the worst kind could find a position at this point and I think that a tragedy."

"This difficulty — am I a mathematician because my degree says so? Am I an engineer because I'm interested in things? Am I a social scientist because I don't think there's a difference between the turbulence in stock markets in terms of unpredictability? At IBM I wouldn't have to worry about that. The names of departments were totally strange and totally meaningless, so it looked like a promising situation for a short time. As it turned out I was going to spend thirty-five years and twelve days at IBM, almost from the beginning to the day when IBM decided that successful research was no longer going to be carried on in that division."

"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."

"Most of the world is of great roughness and infinite complexity. However, the infinite sea of complexity includes two islands of simplicity: one of Euclidean simplicity and a second of relative simplicity in which roughness is present but is the same at all scales."

"Georg Cantor claimed the essence of mathematics lies in its freedom. But mathematicians do not pick problems from thin air for the pleasure of solving them. To the contrary, a mark of greatness resides in the ability to identify the most interesting problems in the framework of what is already known."

"It is beyond belief that we know so little about how people get rich or poor, about how it is they come to dwell in comfort and health or die in penury and disease. Financial markets are the machines in which much of human welfare is decided; yet we know more about how our car engines work than about how our global financial system functions. We lurch from crisis to crisis. In a networked world, mayhem in one market spreads instantaneously to all others—and we have only the vaguest of notions how this happens, or how to regulate it. So limited is our knowledge that we resort, not to science, but to shamans. We place control of the world's largest economy in the hands of a few elderly men, the central bankers."

"People want to see patterns in the world. It is how we evolved. We descended from those primates who were best at spotting the telltale pattern of a predator in the forest, or of food in the savannah. So important is this skill that we apply it everywhere, warranted or not."

"Given the profits he and Pharaoh must have made, one might call Joseph the first international arbitrageur."

"Contrary to popular opinion, mathematics is about simplifying life, not complicating it. A child learns a bag of candies can be shared fairly by counting them out: That is numeracy. She abstracts that notion to dividing a candy bar into equal pieces: arithmetic. Then, she learns how to calculate how much cocoa and sugar she will need to make enough chocolate for fifteen friends: algebra."

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

"My book, The Fractal Geometry of Nature, reproduced Hokusai's print of the Great Wave, the famous picture with Mt. Fuji in the background, and also mentioned other unrecognized examples of fractality in art and engineering. Initially, I viewed them as amusing but not essential. But I changed my mind as innumerable readers made me aware of something strange. They made me look around and recognize fractals in the works of artists since time immemorial. I now collect such works. An extraordinary amount of arrogance is present in any claim of having been the first in "inventing" something. It's an arrogance that some enjoy, and others do not. Now I reach beyond arrogance when I proclaim that fractals had been pictured forever but their true role remained unrecognized and waited for me to be uncovered."

"A branch of physics that I was working in for many years has lately become much less active. Many problems have been solved and others are so difficult that nobody knows what to do about them. This means that I do much less physics today than 15 years ago. By contrast, fractal tools have plenty to do. There is a joke that your hammer will always find nails to hit. I find that perfectly acceptable. The hammer I crafted is the first effective tool for all kinds of roughness and nobody will deny that there is at last some roughness everywhere."

"When the weather changes and hurricanes hit, nobody believes that the laws of physics have changed. Similarly, I don't believe that when the stock market goes into terrible gyrations its rules have changed. It's the same stock market with the same mechanisms and the same people."

"Do I claim that everything that is not smooth is fractal? That fractals suffice to solve every problem of science? Not in the least. What I'm asserting very strongly is that, when some real thing is found to be un-smooth, the next mathematical model to try is fractal or multi-fractal. A complicated phenomenon need not be fractal, but finding that a phenomenon is "not even fractal" is bad news, because so far nobody has invested anywhere near my effort in identifying and creating new techniques valid beyond fractals. Since roughness is everywhere, fractals — although they do not apply to everything — are present everywhere. And very often the same techniques apply in areas that, by every other account except geometric structure, are separate."

"Smooth shapes are very rare in the wild but extremely important in the ivory tower and the factory, and besides were my love when I was a young man. Cauliflowers exemplify a second area of great simplicity, that of shapes which appear more or less the same as you look at them up close or from far away, as you zoom in and zoom out. Before my work, those shapes had no use, hence no word was needed to denote them. My work created such a need and I coined "fractals.""

"A cauliflower shows how an object can be made of many parts, each of which is like a whole, but smaller. Many plants are like that. 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."

"To appreciate the nature of fractals, recall Galileo's splendid manifesto that "Philosophy is written in the language of mathematics and its characters are triangles, circles and other geometric figures, without which one wanders about in a dark labyrinth." Observe that circles, ellipses, and parabolas are very smooth shapes and that a triangle has a small number of points of irregularity. Galileo was absolutely right to assert that in science those shapes are necessary. But they have turned out not to be sufficient, "merely" because most of the world is of infinitely great roughness and complexity. However, the infinite sea of complexity includes two islands: one of Euclidean simplicity, and also a second of relative simplicity in which roughness is present, but is the same at all scales."

"How could it be that the same technique applies to the Internet, the weather and the stock market? Why, without particularly trying, am I touching so many different aspects of many different things? A recent, important turn in my life occurred when I realized that something that I have long been stating in footnotes should be put on the marquee. I have engaged myself, without realizing it, in undertaking a theory of roughness. Think of color, pitch, heaviness, and hotness. Each is the topic of a branch of physics. Chemistry is filled with acids, sugars, and alcohols; all are concepts derived from sensory perceptions. Roughness is just as important as all those other raw sensations, but was not studied for its own sake. … I was not particularly precocious, but I'm particularly long-lived and continue to evolve even today. Above a multitude of specialized considerations, I see the bulk of my work as having been directed towards a single overarching goal: to develop a rigorous analysis for roughness. At long last, this theme has given powerful cohesion to my life … my fate has been that what I undertook was fully understood only after the fact, very late in my life."

"When you seek some unspecified and hidden property, you don't want extraneous complexity to interfere. In order to achieve homogeneity, I decided to make the motion end where it had started. The resulting motion biting its own tail created a distinctive new shape I call Brownian cluster. … Today, after the fact, the boundary of Brownian motion might be billed as a "natural" concept. But yesterday this concept had not occurred to anyone. And even if it had been reached by pure thought, how could anyone have proceeded to the dimension 4/3? To bring this topic to life it was necessary for the Antaeus of Mathematics to be compelled to touch his Mother Earth, if only for one fleeting moment."

"I always saw a close kinship between the needs of "pure" mathematics and a certain hero of Greek mythology, Antaeus. The son of Earth, he had to touch the ground every so often in order to reestablish contact with his Mother; otherwise his strength waned. To strangle him, Hercules simply held him off the ground. Back to mathematics. Separation from any down-to-earth input could safely be complete for long periods — but not forever. In particular, the mathematical study of Brownian motion deserved a fresh contact with reality."

"One of my conjectures was solved in six months, a second in five years, a third in ten. But the basic conjecture, despite heroic efforts rewarded by two Fields Medals, remains a conjecture, now called MLC: the Mandelbrot Set is locally connected. The notion that these conjectures might have been reached by pure thought — with no picture — is simply inconceivable."

"For many years I had been hearing the comment that fractals make beautiful pictures, but are pretty useless. I was irritated because important applications always take some time to be revealed. For fractals, it turned out that we didn't have to wait very long. In pure science, fads come and go. To influence basic big-budget industry takes longer, but hopefully also lasts longer."