Why such big discrepancies? Ponder the typical politician's diagnosis and prognosis for the economy. It generally isolates one or two factors as the cause of this or that malady, pays little attention to the systematic connections among variables, and offers a few pat nostrums about the future. You might never guess from hearing such homilies that tax and interest rates have a complicated impact on unemployment and revenues; that the repercussions of, say, health care reform or an overhaul of welfare are murky at best; or that an increase in some index might feed back on another, reinforcing (or weakening) it and being in turn reinforced (or weakened) by it.

The relatively new mathematical discipline of chaos theory and the associated notion of a non-linear dynamical system are of some relevance to these economic complexities. They help clarify not only some physical and biological phenomena but also why humblingly many of the consequences of NAFTA, environmental laws, Medicare changes, options and derivatives trading, flat tax proposals, and the Contract with America are likely to be unintended. Political hot air to the contrary, the economic climate in 2002 isn't any easier to predict than is the weather in Washington seven years from today. The Democrats' 10 year projections are even more nebulous.

One of the salient ideas of chaos theory can be illustrated with a billiard table on which approximately thirty round obstacles have been fastened in haphazard placement. Ask the best pool player you can find to place a billiard ball at any spot on the table. Then have him (or her) aim toward the obstacles and predict the exact trajectory of the shot. Forecasting the first three or four caroms will usually pose little problem. Even if he's off by the merest fraction of a degree in his reckoning, however, his mis- estimation will be greatly magnified by successive hits of the obstacles. Soon the ball will run up against an obstacle that it wasn't supposed to hit or miss one that it was supposed to hit, and all bets will be off.

The sensitivity of the billiard ball's path to minuscule variations in its initial angle is suggestive of the disproportionate effect of seemingly inconsequential events - the missed planes, serendipitous meetings, and odd mistakes that shape and reshape our public and private lives. The amplification of these slight deviations is just one of the factors explaining why nonlinear dynamical systems are so resistant to dependable and accurate long-range forecast (from which it shouldn't be inferred that no forecasts are possible; it shouldn't take much clairvoyance to foresee that ending the welfare entitlement and reducing the amount of money going to the states in block grants will result in more children going without). This should interest pols as well as pool players, Billary watchers as well as billiards fans. Dynamical systems are, after all, mathematical models of real systems such as the weather, the human immune system, or the economy. They're governed by rules - not always known - that say, in effect, that "if something is currently at a point x, then, given this, that, and the other, it moves on to point y, next to point z, and so on," and these rules are termed nonlinear if, for example, the variables involved are squared or multiplied together rather than simply added or subtracted. Significantly, the elements of such nonlinear systems are not linked as they are in linear sytems such as simple thermometers or bathroom scales. Doubling the magnitude of one part will not double that of another; outputs may, in fact, be grossly disproportionate to inputs.

Even a vague, intuitive understanding of the behavior of so many nonlinearly interacting variables, sensitively dependent systems, feedback, and so on, should be sufficient to arouse a certain wariness of simplistic pronouncements delivered with overweening confidence. (Supply your own names.) From the calculation of the consumer price index to the wildly disparate projections of the deficit by the Congressional Budget Office and the Office of Management and Budget, our standard economic statistics are notoriously imprecise and unreliable; moreover, this imprecision and unreliability (like the billiard ball above) propagate through the system. Our political focus is generally on single causes and scapegoats when the real economic story is usually one of systems and processes. Our assumption that expectations in the stock market exist in a vacuum ignores their frequently self-fulfilling nature. And our belief that welfare, education, and other policies on the federal level will work the same way when proportionally scaled down to the state level is unwarranted by experience.

Lest I be accused of ignoring my own admonition about simplistic declarations, I should mention that there is a large body of research, both mathematical and empirical, that supports these assertions. Mathematical models of the economy, for example, are only very awkwardly cast in a linear framework in which proportionality reigns. The variables in realistic models interact in strongly nonlinear ways that give rise to the phenomena alluded to above. Linear models are used regularly not because they are more accurate, but because they are easier to handle mathematically. (This is another instance of the old saw about the drunkard looking for his keys not where they're likely to be, but where the light is better.)

Furthermore, empirical studies by many researchers suggest that chaos can be induced in the laboratory. Simulated production and distribution systems with mock factories, wholesalers, and retailers have been set up with plausible constraints placed on orders, inventory, and the like. Asked to play this business game realistically, managers and trainees often interact in such a way as to produce chaos - irregular, unpredictable variations in inventory, huge time lags in fulfilling orders, and extreme sensitivity to small changes in conditions. Sounds a little like Congress.

Interestingly, chaos theory also hints at some constructive, albeit vague ideas for partially managing the economy. One is that real change in a system often requires a reorganization of its structure. Another is that to effect such change we must search for points of maximum leverage, points that are often not obvious and are sometimes many steps removed from their intended effects. (Think of the impact that the modification in deposit insurance and interest-rate regulation had on the savings and loans industry.) A third idea is that there is evidence indicating some chaos is necessary for the stability and resilience of systems.

It's always dangerous to apply technical results outside their original domain, especially when much mathematical work remains to be done. Nevertheless, I think chaos theory (and much else) counsels that skepticism should guide us when evaluating the possible consequences, whether glorious or horrendous, of complex economic policies. Much simpler systems involving very few variables and governed by elementary laws are skittishly unpredictable.