Quotes from Benoît B. Mandelbrot

For a thinking person, the most serious mental illness is not being sure of who you are.

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.

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

A man is known by his heroes.

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

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

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.

For a complex natural shape, dimension is relative. It varies with the observer. The same object can have more than one dimension, depending on how you measure it and what you want to do with it. And dimension need not be a whole number; it can be fractional. Now an ancient concept, dimension, becomes thoroughly modern.

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

Since algebra derives from the Arabic jabara = to bind together, fractal and algebra are etymological opposites!)

Some economists, when thinking about long memory, are concerned that it undercuts the Efficient Market Hypothesis that prices fully reflect all relevant information; that the random walk is the best metaphor to describe such markets; and that you cannot beat such an unpredictable market. Well, the Efficient Market Hypothesis is no more than that, a hypothesis. Many a grand theory has died under the onslaught of real data.

Be that as it may, for our present purposes, a bottom line emerges: Stock prices are not independent. Today's action can, at least slightly, affect tomorrow's action. The standard model is, again, wrong.

In economics, there can never be a "theory of everything." But I believe each attempt comes closer to a proper understanding of how markets behave.

But his observations of two forms of wildness remain: abrupt change, and almost-trends. These are the two basic facts of a financial market, the facts that any model must accommodate.

If you can distill the essence of GE's stock behavior over the past twenty years, then you can apply it to financial engineering. You can estimate the risk of holding the stock over the next twenty years. You can estimate how many shares of the stock to buy for your portfolio. You can calculate the proper value of options you want to trade on the stock.

In an ever-more complex world, Mandelbrot argues, scientists need both tools: image as well as number, the geometric view as well as the analytic. The two should work together. Visual geometry is like an experienced doctor's savvy in reading a patient's complexion, charts, and X-rays. Precise analysis is like the medical test results-the raw numbers of blood pressure and chemistry. "A good doctor looks at both, the pictures and the numbers. Science needs to work that way too," he says.

There is a rich vein of jokes about economists and their assumptions. Take the old one about the engineer, the physicist, and the economist. They find themselves shipwrecked on a desert island with nothing to eat but a sealed can of beans. How to get at them? The engineer proposes breaking the can open with a rock. The physicist suggests heating the can in the sun, until it bursts. The economist's approach: "First, assume we have a can opener....

But the financial industry is supremely pragmatic. While it may genuflect to the old icons, it invests its research dollars in the search for newer, better gods.

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.

Regardless, one cannot help but marvel that the movement of security prices, the motion of molecules, and the diffusion of heat could all be of the same mathematical species. As will be seen, it is one of many such strange liaisons in nature.

The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight

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.

Using his models, his computers look for moments when the short-term traders are moving opposite to the long-term investors-and then he bets that the imbalance will correct itself.