Benoit Mandelbrot Quotes

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

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.

"In the end, he says, his goal is to make the financial system work better and more safely. If the real market worked liked FXTrade, costs would come down, liquidity would rise. "The world economy is like your body," he says. "Your heart pumps six liters of blood a minute, and so if you weigh eighty kilos it would take about fifteen minutes to pump your body's weight. By that analogy, the world foreign exchange markets should be transacting $40 trillion every ten minutes. Today we do $1 trillion or so in twenty-four hours. My claim is the global economy is close to a heart attack.

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.

Time does not run in a straight line, like the markings on a wooden ruler. It stretches and shrinks, as if the ruler were made of balloon rubber. This is true in daily life: We perk up during high drama, nod off when bored. Markets do the same.

"Society was not a "social pyramid" with the proportion of rich to poor sloping gently from one class to the next. Instead, it was more of a "social arrow"- very fat at the bottom where the mass of men live, and very thing at the top where sit the wealthy elite. Nor was this effect by chance; the data did not remotely fit a bell curve, as one would expect if wealth were distributed randomly. It is a social law, he wrote: something "in the nature of man.

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

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

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.

"Society was not a "social pyramid" with the proportion of rich to poor sloping gently from one class to the next. Instead, it was more of a "social arrow"- very fat at the bottom where the mass of men live, and very thing at the top where sit the wealthy elite. Nor was this effect by chance; the data did not remotely fit a bell curve, as one would expect if wealth were distributed randomly. It is a social law, he wrote: something "in the nature of man.

That something, though expressed in a neat equation, is harsh and Darwinian, in Pareto's view. At the very bottom of the wealth curve, he wrote, men and women starve and children die young. In the broad middle of the curve all is turmoil and motion: people rising and falling, climbing by talent or luck and falling by alcoholism, tuberculosis, or other forms of unfitness. At the very narrow top sit the elite of the elite, who control wealth and power for a time-until they are unseated through revolution or upheaval by a new aristocratic class. There is not progress in human history. Democracy is a fraud. Human nature is primitive, emotional, unyielding. The smarter, abler, stronger, and shrewder take the lion's share. The weak starve, lest society become degenerate: One can, Pareto wrote, "compare the social body to the human body, which will promptly perish if prevented from eliminating toxins." Inflammatory stuff-and it burned Pareto's reputation. At his death in 1923, Italian fascists were beatifying him, republicans demonizing him. British philosopher Karl Popper called him the "Theoretician of totalitarianism."

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.

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.

I found myself in the position of that child in a story who noticed a bit of string and - out of curiosity - pulled on it to discover that it was just the tip of a very long and increasingly thick string...and kept bringing out wonders beyond reckoning

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."