The hottest new topic in mathematics, physics, and allied sciences is "chaos theory." It is radical in its implications, but no one can accuse its practitioners of being anti- mathematical, since its highly complex math, including advanced computer graphics, is on the cutting edge of mathematical theory.
In a deep sense, chaos theory is a reaction against the effort, hype, and funding that have, for many decades, been poured into such fashionable topics as going ever deeper inside the nucleus of the atom, or ever further out in astronomical speculation. Chaos theory returns scientific focus, at long last, to the real "microscopic" world with which we are all familiar.
It is fitting that chaos theory got its start in the humble but frustrating field of meteorology. Why does it seem impossible for all our hot-shot meteorologists, armed as they are with ever more efficient computers and ever greater masses of data, to predict the weather?
Two decades ago, Edward Lorenz, a meteorologist at MIT stumbled onto chaos theory by making the discovery that ever so tiny changes in climate could bring about enormous and volatile changes in weather. Calling it the Butterfly Effect, he pointed out that if a butterfly flapped its wings in Brazil, it could well produce a tornado in Texas.
Since then, the discovery that small, unpredictable causes could have dramatic and turbulent effects has been expanded into other, seemingly unconnected, realms of science.
The conclusion, for the weather and for many other aspects of the world, is that the weather, in principle, cannot be predicted successfully, no matter how much data is accumulated for our computers. This is not really "chaos" since the Butterfly Effect does have its own causal patterns, albeit very complex. (Many of these causal patterns follow what is known as "Feigenbaum's Number.")
But even if these patterns become known, who in the world can predict the arrival of a flapping butterfly?
The upshot of chaos theory is not that the real world is chaotic or in principle unpredictable or undetermined, but that in practice much of it is unpredictable. And in particular that mathematical tools such as the calculus, which assumes smooth surfaces and infinitesimally small steps, is deeply flawed in dealing with much of the real world. (Thus, Benoit Mandelbroit's "fractals" indicate that smooth curves are inappropriate and misleading for modeling coastlines or geographic surfaces.)
Chaos theory is even more challenging when applied to human events such as the workings of the stock market. Here the chaos theorists have directly challenged orthodox neoclassical theory of the stock market, which assumes that the expectations of the market are "rational," that is, are omniscient about the future. If all stock or commodity market prices perfectly discount and incorporate perfect knowledge of the future, then the patterns of stock market prices must be purely accidental, meaningless, and random ("random walk"), since all the underlying basic knowledge is already known and incorporated into the price.
The absurdity of believing that the market is omniscient about the future, or that it has perfect knowledge of all "probability distributions" of the future, is matched by the equal folly of assuming that all happenings on the real stock market are "random," that is, that no one stock price is related to any other price, past or future. And yet a crucial fact of human history is that all historical events are interconnected, that cause and effect patterns permeate human events, that very little is homogeneous, and that nothing is random.
With their enormous prestige, the chaos theorists have done important work in denouncing these assumptions, and in rebuking any attempt to abstract statistically from the actual concrete events of the real world. Thus, the chaos theorists are opposed to the common statistical technique of "smoothing out" the data by taking twelve-month moving averages of monthly data-whether of prices, production, or employment. In attempting to eliminate jagged "random elements" and separate them out from alleged underlying patterns, orthodox statisticians have been unwittingly getting rid of the very real-world data that need to be examined.
These are but a few of the subversive implications that chaos science offers for orthodox mathematical economics. For if rational expectations theory violates the real world, then so too does general equilibrium, the use of the calculus in assuming infinitesi mally small steps, perfect knowledge, and all the rest of the elaborate neoclassical apparatus.
The neoclassicals have for a long while employed their knowledge of math and their use of advanced mathematical techniques as a bludgeon to discredit Austrians; now comes the most advanced mathematical theorists to replicate, unwittingly, some of the searching Austrian critiques of the unreality and distortions of orthodox neoclassical economics.
In the current mathematical pecking order, fractals, non-linear thermodynamics, the Feigenbaum number, and all the rest rank far higher than the old-fashioned techniques of the neo-classicals.
This does not mean that all the philosophical claims for chaos theory must be swallowed whole--in particular, the assertions of some of the theorists that nature is undetermined, or even that atoms or molecules possess "free will." But Austrians can hail the chaos theorists in their invigorating assault on orthodox mathematical economics from within.
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