Dinosaurs seem perennially popular. They appear on the side of buses, advertising the Natural History Museum. The Daily Telegraph used them in a national advertising campaign. Television programs like Walking With Dinosaurs use animation to build up a storyline with "realistic" looking creatures. The toy shops are full of them. Much of the current interest may stem from the great box-office success of the film Jurassic Park, and appearance of the sequel.

I never saw the original film, but I did read the book soon after it was published. It was a good story, but what I found really interesting was the fact that the plot depended on two frontier areas of scientific research - genetic engineering and chaos theory. Of the two, it is chaos theory that is the less well-known and less understood. What is it all about?

A strictly scientific definition of the phenomenon called "chaos" is "stochastic behaviour occurring in a deterministic system". To put it in a colloquial language, it refers to "apparently lawless behaviour governed entirely by law" ("law" here, of course, meant in the scientific sense).

Chaotic systems are systems which appear to behave in a random fashion but whose behaviour is in fact governed by deterministic physical laws which can be expressed in ordinary, and sometimes quite simple, mathematical equations. The reason for the apparently random behaviour is the fact that, at least under some conditions, the system is very sensitive to tiny changes in the factors which affect its behaviour. As a result barely perceptible changes in one or more of these factors produce major, apparently inexplicable changes in the system.

One of the first areas in which chaos, in this scientific sense, was recognised was weather systems (surprise! surprise!). Its original discoverer, Edward Lorenz, called it "the butterfly effect", because, he said (half jokingly!) the perturbation caused today in New York in a weather system by the flapping of a butterfly's wings might cause a tornado in Wyoming a few days later. Lorenz was working with a very simplified mathematical model of a weather system, with only three variable factors. What he discovered, to his astonishment, was that what was sometimes a "well-behaved" system (ie its behaviour was easily predicted) could flip over into states which were so sensitive to minor changes in the variable factors that they were in practice unpredictable, although still governed by the same mathematical equations which applied when the system was "well-behaved". Unfortunately meteorologists cannot take into account the behaviour of butterflies, birds, bees and other flying creatures when doing their weather forecasting. No wonder long-range forecasts are unreliable! Fortunately, real weather systems seem to be fairly well-behaved over short term spans.

Chaos has been recognised in a wide range of systems: the turbulent flow of fluids, the irregular beating of the heart in certain medical conditions, the strange variations in the population size of some wild creatures, the motion of Hypertension, one of Saturn's moons... and so on.

Some writers in the science/religion area have suggested that chaos has important theological implications. One suggestion is that it gives physical systems a kind of "free-will" over against God because their long-term behaviour is in practice unpredictable. They even hint that this might be an explanation for "natural evils" such as tornados. However, it seems to me that this is misguided. From our point of view, chaotic systems present us with two problems. The first of these is the inability to measure with sufficient accuracy the factors which cause the major changes in the system. Just a s a tiny change in the factor causes a big change in the system, so a tiny error in the measurement causes a big error in the prediction. The result is a system which is, for all practical purposes, unpredictable. Related to this is the fact that, even given sufficient accurate information, the processing of it with sufficient accuracy would require computers with far greater capacity than we are ever likely to have. Does God suffer from these problems? Cannot the God who knows when a sparrow falls know when a butterfly flaps its wings? Surely an infinite God has an infinite capacity to process information? It seems to me that those who appeal to chaos as an answer to the very problem of "natural evils" fail to take seriously what it means for God to be an infinite being.

I think the theological significance of chaotic systems may lie elsewhere. It may be that God created a world in which there are systems as a way of setting some limits to our ability to control, and so exploit, his creation. It is true that the limits seem to be very wide. We have exerted a good deal of control over creation, some of it in a very exploitive way. But here chaotic systems may come into play in another way. They may also be part of what I call God's "negative providence", provision for some "come-back" on us when we do abuse his creation. Some meteorologists think that one possible result of what we are doing to the earth's atmosphere by pollution and global warming is that it will be pushed into chaotic states more often, with unpleasant results for us. Might not this be a form of God's judgement on us? If so we may also see an aspect of his grace in leading scientists to discover the existence of chaotic systems, and understand something about them, in time for us to appreciate what might happen if we do not take steps to reduce atmospheric pollution.