Chaos -- Mathematical and Financial

As I write this, the impact of the $700 billion rescue plan is uncertain, but I strongly suspect it will still be uncertain long after this column appears.

In fact, the uncertainty that usually accompanies complex proposals is what this column is about -- that and the wisdom of acknowledging this uncertainty.

The most honest and productive answer to questions about the effects of economic policy is rarely heard: "Duh, I don't know."

Of course, it's well-known that political and economic affairs are not very predictable, but in addition to all the traditional reasons for this fact are some surprising mathematical ones as well.

These mathematical reasons are deep and ensure that much (not all, of course) of economic and political commentary and forecast is empty. It's usually after-the-fact and no more on target than the farmer/marksman who had hundreds of bull's-eyes on the wall of his barn each with a bullet hole in its center. When asked how he did it, the farmer admitted that he first made the shot and afterward drew the bull's-eye around it.

Football Commentary Versus Simplistic Economic Analysis

Consider the typical analysis of the economy. It generally isolates one or two factors (or their absence) as the cause of this or that malady. There is generally more sophistication in football play-by-play broadcasting.

In general, too little notice is taken of the interconnectedness of the variables in question. Interest rates have an impact on unemployment rates which in turn influence revenues; to a varying extent budget deficits affect trade deficits, which sway interest rates and exchange rates; consumer confidence may rouse the stock market (and vice versa), which alters other indices; natural business cycles of various periods are superimposed on one another; an increase in some quantity or index positively (or negatively) feeds back on another, reinforcing (weakening) it and being in turn reinforced (weakened) by it.

These as well as lax or non-existent regulation and a myriad of other complicating and interacting factors characterize the economy.

The situation is made even worse by a lack of transparency. One reason for the present credit crunch crisis is that banks and investors were not always aware of which mortgages were in the particular packages being offered as securities and, hence, of what risks they were assuming.

Ironically the proposed solution to the problem -- the bailout -- is, at least at this writing, also almost completely opaque.

Secretary of the Treasury Henry Paulson initially put together a three-page proposal devoid of details and then had the temerity to request $700 billion with no judicial or legislative oversight!

It is likely that this proposed financial shock and awe wouldn't have been any more effective than the military version, but neither can we be sure about the considerable revision and expansion of the bill passed on Friday.

Chaos, Pool Tables and the Economy

The mathematical discipline usually referred to as chaos theory and the associated notion of a non-linear dynamical system are relevant to these economic complexities.

Don't run away. I'll skip the defintion of such a system and simply illustrate it, as I have before, with an example -- a pool table on which approximately 30 round obstacles have been fastened in haphazard placement.

Ask an ace pool player to place a 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 bounces and caroms of the ball will usually be easy. 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 round obstacles.

Soon the pool ball will run up against an obstacle that the player didn't intend to hit or miss one that he did intend to hit, and then all bets about where the ball will go are off.

The sensitivity of the ball's path to tiny variations in its initial angle is suggestive of the disproportionate effect of seemingly inconsequential events and actions. The amplification of these slight deviations is just one of the factors explaining why nonlinear dynamical systems -- and the economy is one -- are so resistant to dependable and accurate long-range forecast.

To push the policy maker/pool player analogy a bit further, we can interpret the effect of the opacity and minimal regulation of mortgage securities as perhaps akin to the effect of hand tremors on the pool player. Both lead to less control and even greater unpredictability of the ball/policy's trajectory.

Doubt, Certitude, and Competence

Dynamical systems are generally more complicated than the pool table example, but even a vague, intuitive understanding of their behavior and of the effect 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.

Our standard economic statistics are notoriously imprecise and unreliable, and this imprecision and unreliability (like the pool ball above) quickly propagate through the system.

Interestingly, chaos theory also hints at some constructive, albeit vague ideas for partially managing the economy and even the present bailout.

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.

A third idea is that there is evidence indicating some chaos (in the mathematical sense) is necessary for the stability and resilience of systems.

The bottom line is that when dealing with complex systems we should act with a certain humble dubiousness, not with an unblinking rashness.

A bit of psychology backs up this counsel. A study a few years ago by Cornell psychologist David Dunning found that incompetent people are generally not aware of their own incompetence. Part of the explanation, Dunning wrote, is that the skills that constitute competence are often the very ones needed to recognize incompetence.

This is perhaps why the most clueless politicians are the most self-confident.

Too often in politics, economics, religion, and everyday life, knowledge and tentativeness battle ignorance and certitude.

John Allen Paulos, a professor of mathematics at Temple University, is the author of the best-sellers "Innumeracy" and "A Mathematician Reads the Newspaper," as well as of the just-released "Irreligion: A Mathematician Explains Why The Arguments for God Just Don't Add Up " His "Who's Counting?" column on appears the first weekend of every month.