The Government in Crisis: Scientists seek to take the drama out of a crisis: Comparing Tory backbenchers to cornered dogs may help science to predict how the Government's present crisis will end. William Hartston reports

CATASTROPHE, chaos or crisis? However one describes the Government's difficulties, there is a branch of mathematics created over the past 20 years that deals with it. Sadly for John Major, no theory offers practical advice on how to escape.

Catastrophe Theory was the first attempt, around 1970, to use mathematics to explain sudden, cataclysmic changes. Whether dealing with dramatic changes in economic indicators or the deteriorating morale and collapse of a previously cohesive group, Catastrophe Theory showed how almost imperceptibly gradual changes in the controlling factors can lead to sudden collapse.

One of the earliest examples of its power was in explaining the behaviour of dogs. Simple creatures that they are, dogs are governed by the emotions of fear and anger.

Small increases of one or the other will usually result in small changes of behaviour, but suddenly they may explode into activity, attacking or fleeing. To avoid getting bitten, according to the classical catastrophe theorists, you have to approach the dog in a manner that keeps fear controlling anger. How close you are to it may be less important than the route you took to get there.

Using this principle, we may build a simple model of the behaviour of the Conservative MP, also governed by the fear of an election and the anger of being threatened by the whips. Any action that produces an increase in anger without a commensurate increase in fear could lead to catastrophe.

Catastrophe Theory could also provide a good model of how an apparently smooth energy policy can lead to a sudden need to shut down half the mining industry.

Around 1980, Catastrophe Theory was replaced at number one in the popular maths charts by Chaos Theory. This gave a convincing mathematical basis for what politicians had perhaps suspected all along: that even in the best regulated, accurately measured, physical-law-abiding systems, the most extraordinary things can happen. No matter how precisely you calculate things in advance, there are times when you cannot have the faintest idea of what is going to happen next.

Currently, a great deal of money is being spent on research into potential applications of Chaos Theory in economics. Paradoxically, the general theory may indicate unpredictability, but it can also predict when that unpredictability may occur. Such knowledge could be useful in predicting sudden changes in exchange rates within a monetary system. Nothing practical has yet come out of the research.

Chaos Theory, if appropriate to economic management, would suggest that fine-tuning a healthy economy could, under certain circumstances, lead to total disaster.

The latest idea is Crisis Theory - or Self-Organised Criticality. Developed within the last couple of years, the basic idea is that complex systems tend to settle into a critical state in which anything you do will produce an inter-related series of crises. The simplest example is in piling up dry sand. It settles into a tidy cone; the next handful creates trickles of sand down the sides like a series of tiny earthquakes; then it settles again, ready for the next string of crises.

If the socio-economic structure of the land is governed by Crisis Theory, then it should be no surprise that the economy, the mines, the behaviour of Tory MPs and David Mellor all create their own crises in rapid succession.

There is nothing in the mathematics to say which theory best describes the real world, but in any case the news is not good: Catastrophe Theory might recognise that we are on the brink of a precipice, but the mathematics only show the difficulty in recovering without an intervening disaster; Chaos Theory would point out that we cannot predict what will happen, however far-sighted we may be; and Crisis Theory says it's all going to fall apart anyway.

For the immediate problem of the Maastricht vote, however, Catastrophe Theory seems to give the most appropriate model.

In 1978, Alexander Woodcock and Monte Davis wrote a catastrophic explanation of the collapse into disorder of a social group. The governing factors here are cohesiveness and perceived danger. For a well-trained army, cohesiveness increases with danger, enabling a highly ordered response; for an untrained group, however, a similar increase in perceived danger turns them into a disorganised mob. 'This model,' they wrote, 'makes it easy to see why rumours can be so demoralising. In addition to heightening the perceived danger, they lower cohesiveness by hinting that the 'official version' of events is false - in other words, that the leaders don't even trust their followers with the truth.'

In such circumstances, an army of MPs could turn into a mob.

Tomorrow: the psychology of crisis management