A model can describe the distribution and temporal concentration of return magnitudes without providing a profitable forecast of the direction of future returns.

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I believe it has much to contribute to finance, too. For forty years in fits and starts, as allowed by my personal interests, by unfolding events, and by the availability of colleagues to talk to, the development of fractal geometry has continually interacted with my studies of financial markets and economic systems. I have investigated them not as an economist or financier, but as a mathematical and experimental scientist. To me, all the power and wealth of the New York Stock Exchange or a London currency-dealing room are abstract; they are analogous to physical systems of turbulence in a sunspot or eddies in a river. They can be analyzed with the tools science already has, and new tools I keep adding to the old ones as need and ability allow. With these tools, I have analyzed how income gets distributed in a society, how stock-market bubbles form and pop, how company size and industrial concentration vary, and how financial prices move—cotton prices, wheat prices, railroad and Blue Chip stocks, dollar-yen exchange rates. I see a pattern in these price movements—not a pattern, to be sure, that will make anybody rich; I agree with the orthodox economists that stock prices are probably not predictable in any useful sense of the term. But the risk certainly does follow patterns that can be expressed mathematically and can be modeled on a computer. Thus, my research could help people avoid losing as much money as they do, through foolhardy underestimation of the risk of ruin.

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I see a pattern in these price movements, not a pattern to be sure that will make anybody rich. I agree with the orthodox economists that stock prices are probably not predictable in any useful sense of the term. But the risk certainly does follow patterns that can be expressed mathematically and can be modeled on a computer. Thus, my research could help people avoid losing as much money as they do, through foolhardy underestimation of the risk of ruin. Thinking about markets as a scientific system, we may eventually craft a stronger financial industry and a better system of regulation. A warning to readers here and now. Some of what I say has been embraced as economic orthodoxy in the past decade, But some of it remains contested, ridiculed, even vilified. When I publish in academic journals, as a scientist must, I often stir intense controversy.