Stability and Chaos

Listener: 20 January, 1992

Keywords: History of Ideas, Methodology & Philosophy;

Suppose you were lost in the bush, and wanted to find the sea. One strategy would be to follow a river downhill. It may not be the best way but you do get there. Economists portray market behaviour a bit like this. Here, the objective is an equilibrium between supply and demand. Like the run of the water, the price signals lead you to that endpoint.

But do they? Economists study this in general equilibrium theory, which argues that there is an endpoint, and that market prices point to it; this involves special production processes and an endpoint which is rather restricted, not necessarily the nirvana that enthusiasts suggest. In reaching this equilibrium endpoint people may have starved to death; the theory treats humans as narrow individuals who are not overly concerned with the wellbeing of others.

At this point the reader may say, impatiently, that nobody in their right mind lost in the bush follows the course of a river uncritically. The first thing to do when lost is to sit down, get the pack off your back, and think about the problem. Perhaps boil yourself a billy (use any economics text to light the fire); get out the map; make a plan. You may find there is a track which is easier to follow. Or you may get up onto the ridge, or even over the ridge to the next river , which is not riven by cataracts.

Not only may there be better paths than following the river, but there may be different endpoints. Do you want to end up at the Pacific Ocean or the Tasman (it depends on what side of the divide you start)? How do you know there are not sinkholes like the Dead Sea, or Death Valley, or Harwoods Hole, and that the river never takes you to the sea?

Slavishly following gravity need not be a good strategy. Not that you would ignore the laws of nature, but a bit of planning would be helpful. Might that not also be true for economic management? I leave you to ponder on the problem. Note that we have already included assumptions so familiar they go unstated. For instance, what if the ground is subject to continuing upheavals from earthquakes? Perhaps the economic ground is. Following the market – following any strategy – may be like mimicking a demented mouse running about a maze. Those who reach its end may praise their capabilities, but their success may be solely due to luck. If you find this all too disturbing perhaps you should not read on.

Thus far I have described the physical world. Its laws are familiar; we have known them since our beginnings. They were systematised by Isaac Newton, three centuries ago. It is difficult to appreciate the significance of Newtonianism, which is not just the laws of motion, which have proved powerful predictors. It changed the way we thought about the world. His achievement is summarised in Alexander Pope’s epitaph: “Nature and Nature’s laws lay hid in night: God said Let Newton be! and all was light.’

What Newton suggested was that the physical universe was sufficiently well organised that it could be characterised by some simple ideas, expressed in a mathematical form and used to predict the universe’s behaviour. Einstein never challenged this approach. Relativity involves the same basic ideas; it merely changes some of the equations.

This approach was so powerful it was adopted by many other disciplines. Adam Smith was fascinated by Newtonian mechanics, as were many of the early founders of sociology. Economics and sociology tried to model themselves on it. Economics still does; general equilibrium theory is an example. Its theorists have been awarded more Nobel prizes in economics than those of any other school of thought.

Yet in the last decade a number of pure and applied mathematicians have explored a realm which undermines Newtonianism as a general principle (although it remains useful for most practical purposes). The equations are still there but they no longer predict at all well. Once, small errors did not throw you off the path. We now know that, for some mathematical systems, tiny errors can matter. Nature contains many such systems. Weather forecasting is finding that, despite using some of the world’s most powerful computers, its accuracy is restricted to only days ahead.

If you want to read about this new mathematics, called ‘chaos theory’, try Ian Stewart’s Does God Play Dice? or James Gleick’s Chaos. Let me suggest the feel of it. Suppose two people follow some rule of procedure (such as gravity or market signals) and set out from almost the same spot. Despite adhering to the rules, they could very easily end up in totally different places. In the example I began with this would be understandable if, by accident, our lost trampers happened to be straddling the main divide and so each ended up at different seas. But it appears that these main divides may be just about everywhere. Expressed geographically, ours is a world of strange, beautifully organised terrains, but the contours and paths are incomprehensible in terms of traditional global accounts of the universe. Outcomes are not merely dependent upon process and aptitude; initial position or, if you wish, luck is often crucial.

This ‘chaos’ is not generated by the Heisenberg uncertainty principle of quantum mechanics. Even with perfect causality, one can never know with sufficient precision to be able to predict meaningfully for many purposes

In some ways this column is not merely about economics but about the underlying foundations of Western thought. This is not to predict the collapse of the foundations nor its disciplines. There is as yet nothing to replace them. In the interim we might reflect on the old problems of causality, free will, and perhaps even some deep theological issues.