Benoit Mandelbrot Quotes

"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."

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

Rule 1. Markets are risky.

Rule 2. Trouble runs in streaks.

Rule 3. Markets have a personality.

Rule 4. Markets mislead.

Rule 5. Market time is relative

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.

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."

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.

"No one is alone in this world. No act is without consequences for others. It is a tenet of chaos theory that, in dynamical systems, the outcome of any process is sensitive to its starting point-or, in the famous cliche, the flap of a butterfly's wings in the Amazon can cause a tornado in Texas. I do not assert markets are chaotic, though my fractal geometry is one of the primary mathematical tools of "chaology." But clearly, the global economy is an unfathomably complicated machine. To all the complexity of the physical world of weather, crops, ores, and factories, you add the psychological complexity of men acting on their fleeting expectations of what may or may not happen-sheer phantasms. Companies and stock prices, trade flows and currency rates, crop yields and commodity futures-all are inter-related to one degree or another, in ways we have barely begun to understand. In such a world, it is common sense that events in the distant past continue to echo in the present."

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.

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.

"A key point in my work: Randomness has more than one "state," or form, and each, if allowed to play out on a financial market, would have a radically different effect on the way prices behave. One is the most familiar and manageable form of chance, which I call "mild." It is the randomness of a coin toss, the static of a badly tuned radio. Its classic mathematical expression is the bell curve, or "normal" probability distribution-so-called because it was long viewed as the norm in nature. Temperature, pressure, or other features of nature under study are assumed to vary only so much, and not an iota more, from the average value. At the opposite extreme is what I call "wild" randomness. This is far more irregular, more unpredictable. It is the variation of the Cornish coastline-savage promontories, craggy rocks, and unexpectedly calm bays. The fluctuation from one value to the next is limitless and frightening. In between the two extremes is a third state, which I call "slow" randomness."

"Still, the idea of chance in markets is difficult to grasp, perhaps because, unlike the anonymous particles in a magnet or molecules in a gas, the millions of people who buy and sell securities are real individuals, complex and familiar. But to say the record of their transactions, the price chart, can be described by random processes is not to say the chart is irrational or haphazard; rather, it is to say it is unpredictable. Again, word derivations are helpful. The English phrase "at random" adapts a medieval French phrase, a randon. It denoted a horse moving headlong, with a wild motion that the rider could neither predict nor control. Another example: In Basque, "chance" is translated as zoria, a derivative of zhar, or bird. The flight of a bird, like the whim of a horse, cannot be predicted or controlled."

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.

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.

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.

The whole edifice of modern financial theory is, as described earlier, founded on a few simplifying assumptions. It presumes that homo economicus is rational and self-interested. Wrong, suggests the experience of the irrational, mob-psychology bubble and burst of the 1990's. A further assumption: that price variations follow the bell curve. Wrong, suggests the by-now widely accepted research of me and many others since the 1960's. And now the next assumption wobble: that price variations are what statisticians call i.i.d., independently and identically distributed-like the coin game with each toss unaffected by the last. Evidence for short-term dependence has already been mounting. And now comes the increasingly accepted but still confusing evidence of long-term dependence.