A stochastic description of prices does not require that market participants act without causes; it can model aggregate outcomes when their individual causes and anticipations cannot be reconstructed in time for a decision.

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But they can be described as if they do. And that subtle distinction of thinking about prices as if they were governed by chance has been the dominant, fructifying notion of financial theory for the past 100 years. On its foundation was built the modern global financial industry. Portfolio management, trading strategy, corporate finance, all have been shaped by the chain of assumptions and deductions that succeeding generations of economists and mathematicians have forged from this paradoxical notion of chance. I am, of course, a true believer in the power of probability. I have seen it and applied it in economics, physics, information theory, metallurgy, meteorology, neurology, anatomy, taxonomy, and many other seemingly improbable fields. As a graduate student at the University of Paris more than 50 years ago, I wrote my doctoral thesis on an ignored byway of applied probability, the power law that rules the mathematical frequency with which individual words occur in common language.

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The math for it is straightforward in principle, but in practice, devilish enough for a Nobel Prize. Now, this is an overly simple theory, simpleton, in fact. Fortunately, how and why each individual particle interacts with the next happens to matter less than one may think. We can use this theory to design electrical generators, computer disks, and thousands of other very practical devices. 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, à random.