Cutting the Gordian knot - uncertainty

Since we can never base our decisions on complete knowledge, we have to live with uncertainty

Human existence is fraught with uncertainty. Who knows what tomorrow may bring? But this does not prevent us from taking daily decisions, in our private and public lives, which hold implications for our future, for the future of our families, our country or even - in certain dramatic situations, such as war - the future of humanity as a whole. These decisions, be they good or bad, are taken on the basis of the information available at the time.

This raises the question of whether bad decisions may not be the result of inaccurate or incomplete information. Would complete knowledge of a particular situation allow a fully-informed decision to be taken and its consequences to be predicted with virtual certainty?

The climatological model

The complexity of both natural systems and those of human design means that the ideal scenario - a clear-cut situation leading to a good decision, the effects of which can be simply deduced - is not only unattainable but inconceivable.

An example of such a complex system is provided by that increasingly disturbing climatic conundrum, the greenhouse effect. Does human activity increase the level of carbon dioxide in the atmosphere and, if so, what are the consequences for the earth's climate? From a purely scientific viewpoint, the problem consists in studying the long-term evolution of a complex system (the earth's atmosphere) which is subject to a variety of external influences (cosmic and solar radiation, interactions between the oceans and the land masses, influence of human activity and other life-forms, etc.). The difficulty is twofold: one must first acquire knowledge of the present state of the system and, once this has been thoroughly established, one must then predict its future evolution.

Let us start by examining the apparently simple notion of "the atmospheric level of C[O.sub.2]". Does this mean determining the level of C[O.sub.2] at a particular point in the atmosphere? This requires a statistical analysis which reveals certain major seasonal trends but leaves a substantial margin of error, due to the uncertainty of various meteorological variables. Or does it rather mean, less arbitrarily, the total mass of C[O.sub.2] present in the atmosphere at a given point in time? There is no way of measuring this directly and, in any case, there is no indication that this approach would be any less uncertain than the previous interpretation.

The only precise definition of this parameter would be "the level of C[O.sub.2] at every point in the atmosphere at any given moment". For this definition to be operational, it would have to be supplemented by a mass of data on the direction and strength of the wind, the temperature and humidity of the air, and on the oceans. Only then could we determine, more or less precisely, the near future of the climatic system.

A definition which requires such a volume of information is barely feasible in economic terms. It is therefore right to wonder whether we should not abandon the attempt to produce a single figure to denote this persistently elusive quantity, the "atmospheric level of C[O.sub.2]". Would it not be sufficient to work on the basis of typical figures, for example, from points at intervals of 100 km across the earth's surface, and at 5,000 m intervals of altitude?

The answer naturally depends on precisely what we are looking for. In meteorology, this kind of precision would enable forecasts to be made from one day to the next. To forecast the weather two days ahead, data must be gathered on a finer scale; and the farther ahead we wish to see, the more sensitive and extensive the data base must be. The American meteorologist Edward Lorenz has remarked that a meteorological disturbance which is allowed to develop unhindered may double in magnitude within three days. In the now famous image, a butterfly flapping its wings in the Amazon basin can, if atmospheric conditions are favourable, unleash a storm on the coast of Brittany a year later.

In other words, in order to predict next year's weather at a given spot one would need a network of information on the scale of the butterfly, stretching all over the surface of the globe.

Let us now leave the domain of meteorology, with its short-term quantitative predictions, and return to climatology, where these phenomena are analysed qualitatively over a much longer time-scale. Can we achieve results using composite data, by considering the "atmospheric level of C[O.sub.2]" as a mean annual value adjusted to take account of random fluctuations? This is possible, but it will not guarantee a significant improvement in the degree of certainty of our predictions. One can, of course, imagine large-scale assessments of the thermodynamics of the atmosphere, which would enable definite conclusions to be drawn. The dynamics of the earth's atmosphere are subject to great variation from one year to the next, but a statistical analysis over a longer period - a century, say - would reveal certain trends.

However, the relatively short history of climatology means that such analyses are not available to us at present. In any case, it could be that the atmospheric level of C[O.sub.2] in 100 or 200 years time may crucially depend on phenomena that are too subtle or too obscure to have yet entered our calculations (for example, the disappearance of certain animal species).

A stitch in time

The question of the accumulation of large amounts of data crops up in most human systems (economics, politics, the social sphere, etc.). It was long believed that the state of the economy, and public opinion, were dependent on several major variables (including the rate of inflation, unemployment, taxation and the balance of trade) and that the art of government consisted in maintaining these few indicators within acceptable limits, or bringing them back into line if they strayed beyond these limits.

In recent years, however, some industrialized countries have been unable to reduce their unemployment figures; and a President of the United States suffered a severe electoral defeat during a period of economic growth. It may therefore be wondered whether we tend to represent problems in an over-simplistic manner, and whether statistical data still have any value at all. Perhaps modern societies have become so complex that the reality of a given situation can no longer be encapsulated in a handful of figures, still less be controlled on such a basis.

In any event, we can be certain of one thing in human affairs: that nothing is certain. One might even wonder whether certainty is desirable. To want to know everything about a given subject is futile, an endless escalation into complexity. As Shakespeare's Hamlet knew, any decision involves slicing through a Gordian knot. Complete information will never be available, and total certainty is impossible. But there always comes a moment when one must decide, when the search for further information is more of a hindrance than a help. Certainty will not be forthcoming, either sooner or later, and we will never know for sure whether we have made the right decision: a world in which a different decision had been taken, a world in which Chancellor Helmut Kohl, for example, had not gone ahead with the reunification of Germany, would be so different from the world we know that any comparison between the two is meaningless.

One could almost say that the most important skill in decision-making is knowing when to decide.

IVAR EKELAND, of France, is honorary president of the University of Paris-Dauphine and director of the Institut Finance Dauphine, where he teaches mathematics. His works published in English include The Broken Dice, and Other Mathematical Tales of Chance (Chicago University Press, 1993) and Mathematics and the Unexpected (Chicago University Press, 1988). His most recent publication is Le chaos (Flammarion, Paris, 1994).

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