Benoit Mandelbrot Quotes

Too often, an event’s importance is not recognized until it is too late for proper recording.

How Long Is the Coast of Britain?

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.

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 most-studied evidence, by the greatest number of economists, concerns what is called short-term dependence. This refers to the way price levels or price changes at one moment can influence those shortly afterwards-an hour, a day, or a few years, depending on what you consider "short." A "momentum" effect is at work, some economists theorize: Once a stock price starts climbing, the odds are slightly in favor of it continuing to climb for a while longer. For instance, in 1991 Campbell Harvey of Duke- he of the CFO study mentioned earlier-studied stock exchanges in sixteen of the world's largest economies. He found that if an index fell in one month, it had slightly greater odds of falling again in the next moth, or, if it had risen, greater odds of continuing to rise. Indeed, the data show, the sharper the move in the first, the more likely is is that the price trend will continue into the next month, although at a slower rate. Several other studies have found similar short-term trending in stock prices. When major news about a company hits the wires, the stock will react promptly-but it may keep on moving for the next few days as the news spreads, analysts study it, and more investors start to act upon it."

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.

"In science, all important ideas need names and stories to fix them in the memory. It occurred to me that the market's first wild trait, abrupt change or discontinuity, is prefigured in the Bible tale of Noah. As Genesis relates, in Noah's six hundredth year God ordered the Great Flood to purify a wicked world. Then "were all the fountains of the great deep broken up, and the windows of heaven were opened." Noah survived, of course: He prepared against the coming flood by building a ship strong enough to withstand it. The flood came and went-catastrophic, but transient. Market crashes are like that. The 29.2 percent collapse of October 19, 1987, arrived without warning or convincing reason; and at the time, it seemed like the end of the financial world. Smaller squalls strike more often, with more localized effect. In fact, a hierarchy of turbulence, a pattern that scales up and down with time, governs this bad financial weather. At times, even a great bank or brokerage house can seem like a little boat in a big storm."

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

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.

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

The brain highlights what it imagines as patterns; it disregards contradictory information. Human nature yearns to see order and hierarchy in the world. It will invent it where it cannot find it.

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.

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

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.