A random walk from Paris to Wall Street

Scientists of the so-called reductionist school believe in the explanatory power of hard science. Everything, they argue, from sociology and psychology to biology and chemistry can be understood in terms of elementary-particle physics, the rock-bottom guide to reality. Antireductionists (who sometimes like being called holists) deny this, claiming that all sciences are autonomous and equal. Then there are the radical social constructionists, who stand conventional reductionism on its head by insisting that elementary-particle physics can be reduced to sociology. I used to think they were crazy, but now I'm not so sure.

It turns out that a certain theory long credited to Albert Einstein was actually thought up by a fellow trying to make sense of a rather peculiar social phenomenon of the kind best observed on Wall Street. Despite its social-scientific origins, this theory can explain why elementary particles behave in the unfathomable way they do.

The story starts with a botanist. In 1827 an Englishman named Robert Brown was looking through his microscope at some pollen granules suspended in water. He noticed that they were behaving in an odd manner. They seemed to be doing a sort of drunken dance, moving this way and that without pause or logic. He then observed that soot particles taken from the smoggy London air and put into water acted the same way, as did microscopic particles chipped off the Sphinx. In 1828 he published a pamphlet describing the mysterious phenomenon, which subsequently became known as Brownian motion.

Skip ahead to 1905. That was the year Einstein, seeking to demonstrate the existence of atoms, came up with an elegant argument based on Brownian motion. Those tiny particles that appeared to be rambling aimlessly about, Einstein submitted, were actually getting shoved around by the surrounding water molecules. From his calculations, he derived the square-root law, which says that the average distance traveled by a particle in Brownian motion is proportional to the square root of the time it has been traveling. (Thus, a drunkard wandering at random on Manhattan's street grid could expect to get as far from his starting point in one hundred minutes as a sober person heading straight down an avenue at the same pace would in ten.)

Einstein explained Brownian motion the same year he described the photoelectric effect and proposed the theory of special relativity. The discovery of the square-root law, write Michael White and John Gribbin in Einstein: A Life in Science (1994), was "completely novel."

This, as it turns out, is completely false. The theory of Brownian motion--and the square-root law in particular--had been worked out five years earlier by a young French doctoral candidate in mathematics named Louis Bachelier. He, too, was trying to explain certain puzzling movements: not of pollen granules suspended in water but of stock and bond prices on the Paris Bourse. In Bachelier's theory of speculation, bits of breaking news played the role that molecular collisions would play for Einstein. Bombarded by the unpredictable arrival of such information, stock prices meander in a way that is impossible to foretell. In today's parlance, they take a random walk.

Bachelier dutifully turned in his dissertation on the topic, received a respectable but not superlative mention honorable, and died in provincial obscurity, in 1946. Not long thereafter, however, MIT economist Paul Samuelson and a couple of colleagues stumbled upon Bachelier's thesis, a copy of which had been collecting dust in the school's library. "Bachelier seems to have had something of a one-track mind," Samuelson later wrote. "But what a track!" By the 1960s, a group of professors at MIT, Chicago, and Stanford had elaborated the Frenchman's insights into the notorious efficient-market theory. Thanks to the frenzied activity of competing traders, the theory held, share prices adjust instantly to reflect all available information. Thus tomorrow's performance cannot be determined by anything that is known today.

Wall Streeters hated this new product of the ivory tower. If beating the market was purely a matter of luck, then their vaunted stock-picking skills were worthless. Empirically, however, the efficient-market theory seemed invincible. The history of market fluctuations fit the square-root law to a T. As far as Samuelson was concerned, this was "the best confirmed theory in the social sciences."

For the last act, the scene switches back to physics. Around the same time that Bachelier was being rediscovered by social scientists, a Princeton mathematician named Edward Nelson was trying a little experiment with the theory of Brownian motion. What, he wondered, do you get if you apply its restless logic to classical Newtonian physics? In 1966, he unveiled his astounding answer: You get quantum mechanics.

It's true. If, as Nelson supposed, elementary particles are subjected to a relentless but statistically random jiggling, they end up displaying all the characteristic forms of quantum strangeness. The classical concept of velocity, for example, disappears when the path taken by an electron is infinitely crinkly. Nelson's students were able to extend Brownian reasoning to cover such phenomena as the electron's spin.

Here, then, is the correct chronology. A theory is proposed to explain a mysterious social institution (the Paris Bourse). It is then used to resolve a mid-level mystery in physics (Brownian motion). Finally, it clears up an even deeper mystery in physics (quantum behavior). The implication is plain: Market weirdness explains quantum weirdness, not the other way around.

Think of it this way: If Isaac Newton had worked at Goldman Sachs instead of sitting under an apple tree, he would have discovered the Heisenberg uncertainty principle.


Copyright © 1997 Lingua Franca,Inc. All rights reserved.