Stephen Hawking has said that the science of this 21st century will be the science of complexity. When science has achieved so much, what could it be that could take us all on yet another enormous leap forward?

Science generally uses a system called reductionism to investigate our world. This means breaking down anything being examined into the parts that make it up. From that we can learn how things work. If you take a mechanical clock to pieces you can see what each part does you can find out how it works. Some things, however, can’t be investigated in this way. There is much to be learned by dissecting a rat, for example, but in dissecting it, we kill it and cannot know what gives it life.

Sometimes we need to stand back and look at the whole system to understand how things work, rather than break it into pieces.

Chaos Theory looks at how very simple things can generate very complex outcomes that could not be predicted by just looking at the parts by themselves. You may have noticed the wonderful swirling patterns of birds flying together in the sky or fish schooling in the oceans. At first glance we would think the birds would have to be rather intelligent to work out how to fly in formation like that. We would probably also assume there must be a ‘bird in charge’ giving the others instructions. Research into swarms has shown, however, that all that is required is for each bird to maintain the distance between itself and its neighbours and fly in the average direction of its neighbours. From this alone the wonderful, swirling, complex patterns the birds or fish make are seen. Simple rules can generate complex behaviours that just seem to emerge out of nowhere.

Complexity Theory looks at how complex systems can generate simple outcomes. Consider the billions of cells that make up a person and yet they all manage to work together in such a way that the body works as a single unit. Our body works to keep us alive. We get hungry when we need food; we get thirsty when we need water. We can think and we have a distinct personality. Something happens when large numbers of individual units come together and interact intensely with each other. New levels of operating just emerge through what is called self-organisation. By looking at a single human cell, you could not tell that it would be able to operate with other cells to form a human body.

A city has the same large number of intensely interacting units. This time human beings form the units. Once again, we would not know from examining a single human being that they would gather together in the millions to form cities. It is an emergent property, so that a city takes on a life or a personailty of its own, which has self organised out of the interactions of all the people who live in the city.

We cannot predict what a complex system will evolve into. When we think about it, all life from the smallest cell to the largest animals are complex systems and life always provides us with a mystery .

You can follow your way through the tutorial to learn about some of the many aspects of Chaos and Complexity. Chaos and Complexity is a new science looking at our world in a holistic way. The large number of calculations needed to explore complexity has meant that it is only since the advent of the computer that we have been able to really understand what complexity is all about. With the ever-increasing ability of computers to undertake enormous calculations very quickly, we are making great leaps in our understanding of the complex nature of the world in which we live.